# LaTeX2HTML 95.1 (Fri Jan 20 1995)
# Associate image original text (scrambled) with physical files.

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$key = q/{_inline}$dsigmadt${_inline}/;
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$key = q/{displaymath}I=(b-a)intlimits^+infty_-inftyf(x)p(x)dx{displaymath}/;
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$key = q/{_inline}$frack^3n^2rightarrow0${_inline}/;
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$key = q/{displaymath}0leqsigma_yleqsqrt2tildesigma_y{displaymath}/;
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$key = q/{_inline}$chi^2left(chi^2_rmnew=mboxconst.chi^2_rmoldright)${_inline}/;
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$key = q/{_inline}$leq1${_inline}/;
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$key = q/{_inline}$y=displaystylesum^N_i=1x_i${_inline}/;
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$key = q/{_inline}$lnp_N${_inline}/;
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$key = q/{displaymath}L=prod^N_i=1p_iproptoexpleftlbrace-sum^N_i=1frac(x_i-xi_i)^22sigma^2_irightrbrace{displaymath}/;
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$key = q/{_inline}$chi^2vert_1,2ldots${_inline}/;
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$key = q/{_inline}$[a,b)ldots${_inline}/;
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$key = q/{displaymath}n_rmtot=fracn(A)n(B)n(C){displaymath}/;
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$key = q/{_inline}$beta${_inline}/;
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$key = q/{_inline}$p=0.5${_inline}/;
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$key = q/{_inline}$x_j${_inline}/;
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$key = q/{displaymath}P(BA)=P(AB)fracP(B)P(A){displaymath}/;
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$key = q/{_inline}$f_2=sigma^2-${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img455.gif">'; 
$key = q/{_inline}$M_klmnldots${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img183.gif">'; 
$key = q/{_inline}$lambda_LsimQ${_inline}/;
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$key = q/{_inline}$sqrtp(1-p)n${_inline}/;
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$key = q/{_inline}$rho_00${_inline}/;
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$key = q/{_inline}$sqrtnsigma${_inline}/;
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$key = q/{_inline}$mboxbfa+${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img907.gif">'; 
$key = q/{_inline}$w(x)=F(x)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1482.gif">'; 
$key = q/{displaymath}p_i=frac1sqrt2pisigma_iexpleftlbracefrac-(x_i-xi_i)^22sigma^2rightrbrace{displaymath}/;
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$key = q/{_inline}$I_j-q${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1446.gif">'; 
$key = q/{_inline}$s(y|x)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img144.gif">'; 
$key = q/{_inline}$n(S)${_inline}/;
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$key = q/{displaymath}I_j+1=leftlbrackaI_j+crightrbrackrmmod(m){displaymath}/;
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$key = q/{}psfigfigure=fig24b.phys.ps,clip=true,width=3.75in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1347.gif">'; 
$key = q/{_inline}$lbracex^(i)i=1,Nrbrace${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1358.gif">'; 
$key = q/{displaymath}expleftlbrack-frac12left(g_1^2+g_2^2right)rightrbrackdg_1,dg_2{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1470.gif">'; 
$key = q/{_inline}$kneql${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img179.gif">'; 
$key = q/{_inline}$L_1L_2neq${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img791.gif">'; 
$key = q/{_inline}$Pr{mboxFrankNagysmilesonceandonceonly}${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img423.gif">'; 
$key = q/{_inline}$y_i=${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img465.gif">'; 
$key = q/{_inline}$P_k(t)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img549.gif">'; 
$key = q/{displaymath}leftlangle(b-langlebrangle)(a-langlearangle)rightrangle=-fracz_2sigma^2_1-z_1sigma^2_2left(z_1-z_2right)^2{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img211.gif">'; 
$key = q/{tabular}llr4;SPM_amp;bfMinimization;SPM_amp;1574.1;SPM_amp;StatementofProblem;SPM_amp;1584.2;SPM_amp;DerivativeFormalismfor_inline$chi^2$_inline;SPM_amp;1594.3;SPM_amp;TheDerivativeMethodfor_inline$chi^2$_inline;SPM_amp;1654.4;SPM_amp;TheRealWorldand_inline$chi^2$_inlineMinimization;SPM_amp;168;SPM_amp;;SPM_amp;5;SPM_amp;bfGoodnessofFit;SPM_amp;1805.1;SPM_amp;The_inline$chi^2$_inlineDistribution;SPM_amp;1815.2;SPM_amp;ConfidenceLevel;SPM_amp;1855.3;SPM_amp;Bartlett's_inline$S$_inlineFunction;SPM_amp;1895.4;SPM_amp;HypothesisTesting;SPM_amp;1915.5;SPM_amp;Student's_inline$t$_inlineDistribution;SPM_amp;1945.6;SPM_amp;RobustEstimation;SPM_amp;197;SPM_amp;;SPM_amp;6;SPM_amp;bfGenerationofRandomNumbers;SPM_amp;211{tabular}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img8.gif">'; 
$key = q/{displaymath}fracn(C)n_rmtot=fracn(A)n_rmtotcdotfracn(B)n_rmtot{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img60.gif">'; 
$key = q/{_inline}$w(x)=1-e^-x${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1489.gif">'; 
$key = q/{_inline}$sqrtp(1-p)sqrtNlanglegrangle${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img377.gif">'; 
$key = q/{_inline}$propto${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img727.gif">'; 
$key = q/{_inline}$phantomHere,B${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img57.gif">'; 
$key = q/{displaymath}b_m=sum_ifracx_iC_imsigma^2_i=sum_ifracx_isigma^2_ifracpartialxi_ipartiala_m{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img894.gif">'; 
$key = q/{_inline}$(x,y)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img125.gif">'; 
$key = q/{_inline}$mu=frac1Ndisplaystylesum^N_i=1f(x_i)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1029.gif">'; 
$key = q/{displaymath}M_ml=sum_ifracC_imC_ilsigma^2_i{displaymath}/;
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$key = q/{displaymath}L=expleftlbrack-displaystyleintlimitsp(x),dx,trightrbrackprod^N_i=1p_i,dx_i,t{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img981.gif">'; 
$key = q/{_inline}$(a,b]${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img13.gif">'; 
$key = q/{_inline}$a^*_m${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1037.gif">'; 
$key = q/{_inline}$10^6${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1239.gif">'; 
$key = q/{_inline}$g_2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1476.gif">'; 
$key = q/{}psfigfigure=fig17.phys.ps,clip=true,width=4.0in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1189.gif">'; 
$key = q/{_inline}$xle0${_inline}/;
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$key = q/{_inline}$q_i${_inline}/;
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$key = q/{_inline}$displaystyleint_mboxsmallBINdtfracdsigmadt${_inline}/;
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$key = q/{}psfigfigure=fig19.phys.ps,clip=true,width=4.0in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1225.gif">'; 
$key = q/{displaymath}p(x)=frac1sqrt2pisigmaexpleftlbrace-frac[x-mu]^22sigma^2rightrbrace{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img242.gif">'; 
$key = q/{_inline}$y_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img202.gif">'; 
$key = q/{_inline}$e^-1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img437.gif">'; 
$key = q/{_inline}$P(S)=1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img41.gif">'; 
$key = q/{_inline}$S_iS_j=0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img21.gif">'; 
$key = q/{_inline}$V_x=leftlangle(x-langlexrangle)^2rightrangle=${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img160.gif">'; 
$key = q/{_inline}$lambda_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img952.gif">'; 
$key = q/{_inline}$chi^2left(bf$beta$_0+Deltabetaright)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1223.gif">'; 
$key = q/{_inline}$np=lambda=1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img436.gif">'; 
$key = q/{_inline}$C_j${_inline}/;
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$key = q/{_inline}$+2a_1a_2sigma_1sigma_2rho_12${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img233.gif">'; 
$key = q/{_inline}$mu^*_,rmtrim${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1384.gif">'; 
$key = q/{_inline}$p_N=e^-tLambda(tLambda)^N${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img959.gif">'; 
$key = q/{_inline}$Y_lm${_inline}/;
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$key = q/{_inline}$(x^(i)-mu)sigma^2${_inline}/;
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$key = q/{}psfigfigure=fig20.phys.ps,clip=true,width=4.0in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1235.gif">'; 
$key = q/{_inline}$E_n${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img572.gif">'; 
$key = q/{_inline}$S_1=S${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img25.gif">'; 
$key = q/{_inline}$;SPM_gt;p_max${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1502.gif">'; 
$key = q/{_inline}$mu_i=0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1108.gif">'; 
$key = q/{_inline}$H_1${_inline}/;
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$key = q/{_inline}$Nsim10${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1466.gif">'; 
$key = q/{_inline}$chi^2left(bf$beta$_0right)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1224.gif">'; 
$key = q/{displaymath}sigma^2bigvert_1=frac1N(3-a^2){displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1042.gif">'; 
$key = q/{_inline}$sigma_j${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1164.gif">'; 
$key = q/{}psfigfigure=fig29.phys.ps,clip=true,width=4.0in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1491.gif">'; 
$key = q/{displaymath}I_j=I_j-qoplusI_j-p{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1442.gif">'; 
$key = q/{_inline}$=lambda${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img451.gif">'; 
$key = q/{_inline}$L=expleft(-frac12chi^2right)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img905.gif">'; 
$key = q/{}psfigfigure=fig3.phys.ps,clip=true,width=3.0in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img110.gif">'; 
$key = q/{_inline}$mu_1;SPM_gt;mu_0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1348.gif">'; 
$key = q/{_inline}$S(lambda)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1313.gif">'; 
$key = q/{displaymath}intlimits^+infty_-inftyp(x)dx=1{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img111.gif">'; 
$key = q/{_inline}$=R(j)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1459.gif">'; 
$key = q/{}psfigfigure=fig4.phys.ps,clip=true,width=5.5in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img208.gif">'; 
$key = q/{_inline}$x_1lexlex_2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1499.gif">'; 
$key = q/{}psfigfigure=fig7.phys.ps,clip=true,width=5.5in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img467.gif">'; 
$key = q/{_inline}$P(SA)P(A)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img51.gif">'; 
$key = q/{_inline}$tau^*=tau_0+Oleft(frac1nright)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img740.gif">'; 
$key = q/{displaymath}fraclanglefranglelanglegranglesqrtfrac1Nleftlangleleft(fracflanglefrangle-fracglanglegrangleright)^2rightrangle{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img371.gif">'; 
$key = q/{_inline}$nsim10${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1240.gif">'; 
$key = q/{_inline}$lim_nrightarrowinftyrhoSigma${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img302.gif">'; 
$key = q/{_inline}$f^primeprime${_inline}/;
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$key = q/{displaymath}K(k)=lnvarphi(k){displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img270.gif">'; 
$key = q/{_inline}$p_jk${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img594.gif">'; 
$key = q/{_inline}$=sqrtx_i${_inline}/;
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$key = q/{_inline}$x_1${_inline}/;
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$key = q/{_inline}$1lejleL${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1457.gif">'; 
$key = q/{_inline}$bulletn(B)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img56.gif">'; 
$key = q/{_inline}$(beta)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img501.gif">'; 
$key = q/{_inline}$Oleft(frac1sqrtnright)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img765.gif">'; 
$key = q/{_inline}$E_k${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img597.gif">'; 
$key = q/{displaymath}z^(i)=fracleft(x^(i)-muright)sigma{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1387.gif">'; 
$key = q/{_inline}$B_2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img68.gif">'; 
$key = q/{_inline}$L_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img821.gif">'; 
$key = q/{_inline}$L=exp${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img906.gif">'; 
$key = q/{_inline}$I_0${_inline}/;
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$key = q/{displaymath}fraclanglefranglelanglegranglesqrtfrac1nleftlangleleft(fracflanglefrangle-fracglanglegrangleright)^2rightrangle{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img350.gif">'; 
$key = q/{displaymath}p(x)=frac12piintlimits^+infty_-inftydx,e^-ikxvarphi(k){displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img263.gif">'; 
$key = q/{_inline}$sigma^2=frac1nfraclanglef^2ranglelanglegrangle^2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img806.gif">'; 
$key = q/{_inline}$Lambda=mboxnumber${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img526.gif">'; 
$key = q/{displaymath}sigma^2_yleqleft(|a_1sigma_1|+|a_2sigma_2|right)^2{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img234.gif">'; 
$key = q/{_inline}$gamma${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img716.gif">'; 
$key = q/{_inline}$displaystylesum^M_k=1tildep(k)=1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img948.gif">'; 
$key = q/{_inline}$displaystyleint(f(x)-langlefrangle),(g(x)-langlegrangle),p(x),dx${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1049.gif">'; 
$key = q/{_inline}$p^kq^n-k${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img417.gif">'; 
$key = q/{}psfigfigure=fig25.phys.ps,clip=true,width=5.25in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1357.gif">'; 
$key = q/{_inline}$^2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img196.gif">'; 
$key = q/{_inline}$langleY_lmY_l^primem^primerangleneqlangleY_lmranglelangleY_l^primem^primerangle${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1057.gif">'; 
$key = q/{_inline}$t_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1244.gif">'; 
$key = q/{_inline}$sigma=0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img357.gif">'; 
$key = q/{displaymath}P(AB)=fracP(AB)P(B)=P(A){displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img62.gif">'; 
$key = q/{_inline}$p=120${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img421.gif">'; 
$key = q/{_inline}$sigma^2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1110.gif">'; 
$key = q/{_inline}$dx,dy${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img128.gif">'; 
$key = q/{_inline}$z=f(x)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img158.gif">'; 
$key = q/{_inline}$Re_1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img124.gif">'; 
$key = q/{_inline}$w(F)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1268.gif">'; 
$key = q/{_inline}$F_j${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1142.gif">'; 
$key = q/{}psfigfigure=fig14.phys.ps,clip=true,width=2.75in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1173.gif">'; 
$key = q/{_inline}$lambda_0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1294.gif">'; 
$key = q/{displaymath}0lerle1{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1494.gif">'; 
$key = q/{_inline}$sqrtxi_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img924.gif">'; 
$key = q/{_inline}$cosvarphi_1cosvarphi_2;SPM_lt;0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img703.gif">'; 
$key = q/{_inline}$overlinesigma${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1352.gif">'; 
$key = q/{_inline}$k^2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img274.gif">'; 
$key = q/{_inline}$approxe^-1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img439.gif">'; 
$key = q/{_inline}$p_N${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img958.gif">'; 
$key = q/{_inline}$P_0-1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img552.gif">'; 
$key = q/{displaymath}L=L_1L_2{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img820.gif">'; 
$key = q/{_inline}$a_n_1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img404.gif">'; 
$key = q/{_inline}$Lambdarightarrowppi^-${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1420.gif">'; 
$key = q/{_inline}$frac1Nsigma^2bigvert_m.l.m.${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1045.gif">'; 
$key = q/{_inline}$Pleft(x_ivertTright)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img640.gif">'; 
$key = q/{_inline}$Sigman${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img301.gif">'; 
$key = q/{displaymath}p_iproptoexpleftlbrackfrac-lbracen_i-lambda_itrbrace^2lambda_itrightrbrack{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img961.gif">'; 
$key = q/{_inline}$varphi_x${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img309.gif">'; 
$key = q/{_inline}$S_1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img32.gif">'; 
$key = q/{_inline}$M_x${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img197.gif">'; 
$key = q/{_inline}$dx_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img982.gif">'; 
$key = q/{_inline}$M_ml${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img892.gif">'; 
$key = q/{_inline}$mu=displaystyleintlimits^b_af(x)p(x)dx${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img326.gif">'; 
$key = q/{_inline}$bf$x$${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img191.gif">'; 
$key = q/{displaymath}varphi(k)=1+ilanglexranglek-fraclanglex^2ranglek^22,mboxetc.{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img268.gif">'; 
$key = q/{_inline}$w=h(x,y)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img150.gif">'; 
$key = q/{displaymath}rmerf(x)=frac2sqrtpiintlimits^x_0expleft(-y^2right)dy{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img113.gif">'; 
$key = q/{displaymath}T(XY)=fracPr(XY)Pr(Y)=fracr(x,y)q(y)fracdx,dydy{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img132.gif">'; 
$key = q/{_inline}$bfrho,_kl=M_klsqrtM_kk,M_ll${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img176.gif">'; 
$key = q/{_inline}$Deltabeta_j${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1217.gif">'; 
$key = q/{_inline}$B=B_1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img67.gif">'; 
$key = q/{_inline}$S_2=Y-S=S^*${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img26.gif">'; 
$key = q/{displaymath}mu^*_Am=frac1Nsum^N_i=1x^(i){displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1361.gif">'; 
$key = q/{_inline}$x=-lny${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1480.gif">'; 
$key = q/{_inline}$langlechi^2rangle=k${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1247.gif">'; 
$key = q/{_inline}$lambdadt${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img562.gif">'; 
$key = q/{_inline}$P(k,lambda)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img433.gif">'; 
$key = q/{displaymath}mu=sum^N_i=1mu_i{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1100.gif">'; 
$key = q/{displaymath}langlemu^*_Amrangle=mu{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1365.gif">'; 
$key = q/{_inline}$P_Y^(i)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1326.gif">'; 
$key = q/{_inline}$P_n(t)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img571.gif">'; 
$key = q/{displaymath}p(x)proptoexpleft(-fracxmuright){displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1368.gif">'; 
$key = q/{_inline}$N_rmhist${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img382.gif">'; 
$key = q/{displaymath}fracdP_kdt(t)=-lambdaP_k(t)+lambdaP_k-1(t)hspace1em:kne0{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img551.gif">'; 
$key = q/{_inline}$R(1ldotsL)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1455.gif">'; 
$key = q/{_inline}$P_0(t)=e^-lambdat${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img554.gif">'; 
$key = q/{_inline}$lnL${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1083.gif">'; 
$key = q/{_inline}$varphileft(k_1,k_2right)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img347.gif">'; 
$key = q/{_inline}$pmsqrtN_rmhist${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img381.gif">'; 
$key = q/{displaymath}underbraceht,h,ttldots_n{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img415.gif">'; 
$key = q/{_inline}$y=frac1ndisplaystylesum^n_i=1x_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img250.gif">'; 
$key = q/{_inline}$rho_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img294.gif">'; 
$key = q/{_inline}$lambda_n(t)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img566.gif">'; 
$key = q/{_inline}$fracdydx=|f^prime(x)|${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img121.gif">'; 
$key = q/{_inline}$sqrtN${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1076.gif">'; 
$key = q/{}psfigfigure=fig27.phys.ps,clip=true,width=5.0in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1403.gif">'; 
$key = q/{_inline}$ntimesn${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img193.gif">'; 
$key = q/{_inline}$langlefrangle=0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img805.gif">'; 
$key = q/{displaymath}p(t)=fracGammaleft(fracf+12right)sqrtnpiGammaleft(fracf2right)frac1left(1+fract^2fright)^(f+1)2{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1343.gif">'; 
$key = q/{}psfigfigure=fig5.phys.ps,clip=true,width=4.0in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img216.gif">'; 
$key = q/{displaymath}F(x)=intlimits^x_-inftyp(x)dx{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img104.gif">'; 
$key = q/{}psfigfigure=fig1.phys.ps,clip=true,width=6.5in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img15.gif">'; 
$key = q/{_inline}$proptofrac1sqrtN${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1362.gif">'; 
$key = q/{displaymath}g=fracdisplaystylesum^N_i=1u_i-fracN2sigmasqrtN{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1463.gif">'; 
$key = q/{_inline}$M^-1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1167.gif">'; 
$key = q/{displaymath}I=intlimits^b_af(x)dx{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img316.gif">'; 
$key = q/{_inline}$Pleft(S_1right)+Pleft(S_2right)=P(Y)=1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img27.gif">'; 
$key = q/{_inline}$|a_1sigma_1||a_2sigma_2|neq1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img239.gif">'; 
$key = q/{_inline}$proptomaxleftlbrackfrac1sqrtN,frac1sqrtmrightrbrack${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1440.gif">'; 
$key = q/{_inline}$a_m${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img884.gif">'; 
$key = q/{_inline}$[t,t+dt]${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img544.gif">'; 
$key = q/{_inline}$g_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1469.gif">'; 
$key = q/{_inline}$tildec${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img610.gif">'; 
$key = q/{_inline}$P(BA)=P(B_1A)+P(B_2A)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img70.gif">'; 
$key = q/{_inline}$lambda=N3600${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img533.gif">'; 
$key = q/{_inline}$rmerror^2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1039.gif">'; 
$key = q/{}psfigfigure=fig16.phys.ps,clip=true,width=2.5in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1187.gif">'; 
$key = q/{_inline}$existsmboxprobabilityp=N3600${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img529.gif">'; 
$key = q/{_inline}$np=lambda${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img428.gif">'; 
$key = q/{_inline}$y_1+y_2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img484.gif">'; 
$key = q/{_inline}$langlef(x)rangle=displaystyleintlimits^infty_-inftyf(x)p(x)dx${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img156.gif">'; 
$key = q/{_inline}$w_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1531.gif">'; 
$key = q/{_inline}$(f=n-1)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1341.gif">'; 
$key = q/{_inline}$N_T${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1073.gif">'; 
$key = q/{_inline}$expleft(-fracchi^22right)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1260.gif">'; 
$key = q/{_inline}$e^-x${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1488.gif">'; 
$key = q/{_inline}$lambda_n=lambda${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img583.gif">'; 
$key = q/{_inline}$e_1ldotse_N${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1098.gif">'; 
$key = q/{_inline}$mu=sum^n_i=1mu_in${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img299.gif">'; 
$key = q/{_inline}$oplus=${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1443.gif">'; 
$key = q/{_inline}$omega_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1109.gif">'; 
$key = q/{_inline}$I_j${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1428.gif">'; 
$key = q/{_inline}$|a_1sigma_1|=|a_2sigma_2|${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img238.gif">'; 
$key = q/{_inline}$sigma^2=displaystyleintlimits^b_af^2(x)p(x)dx-mu^2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img328.gif">'; 
$key = q/{_inline}$mu^*_Am${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1383.gif">'; 
$key = q/{_inline}$a_lm${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1056.gif">'; 
$key = q/{displaymath}frac1sigma^2sum^N_i=1left(x^(i)-mu^*_Lright)=0{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1396.gif">'; 
$key = q/{_inline}$q(y)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img116.gif">'; 
$key = q/{displaymath}left(arrayc10001arrayright)frac11000left(frac9991000right)^999=leftlbrackfrac9991000rightrbrack^999{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img438.gif">'; 
$key = q/{displaymath}bleft(k,n,fraclambdanright)=fracn!k!(n-k)!left(fraclambdanright)^kleft(1-fraclambdanright)^n{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img429.gif">'; 
$key = q/{_inline}$E_n=n${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img588.gif">'; 
$key = q/{_inline}$Pr(y=mboxintegerr)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img444.gif">'; 
$key = q/{_inline}$n_T${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img837.gif">'; 
$key = q/{_inline}$mu${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img255.gif">'; 
$key = q/{_inline}$lambda_1ldotslambda_L${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1218.gif">'; 
$key = q/{_inline}$E_nrightarrowE_n+1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img563.gif">'; 
$key = q/{_inline}$rho_10${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img866.gif">'; 
$key = q/{_inline}$displaystylesum^k_i=1x^2_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1257.gif">'; 
$key = q/{_inline}$d(w)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img151.gif">'; 
$key = q/{tabular}llr1;SPM_amp;bfBasicDefinitionsandResults;SPM_amp;51.1;SPM_amp;BasicDefinitionsandResults;SPM_amp;61.2;SPM_amp;BayesTheorem;SPM_amp;111.3;SPM_amp;ContinuousDistributions;SPM_amp;201.4;SPM_amp;FunctionsofaRandomVariable;SPM_amp;231.5;SPM_amp;PropertiesofJointDistributionFunctions;SPM_amp;271.6;SPM_amp;Means,Moments,Correlations;SPM_amp;291.7;SPM_amp;CentralLimitTheorem;SPM_amp;43;SPM_amp;;SPM_amp;2;SPM_amp;bfFeefoefuminLasVegas:;SPM_amp;62;SPM_amp;bfCombinatoricandDiscreteProbability;SPM_amp;2.1;SPM_amp;BinomialandPoissonDistributions;SPM_amp;632.2;SPM_amp;BirthandDeathProcesses;SPM_amp;78;SPM_amp;;SPM_amp;3;SPM_amp;bfEstimationofParameters;SPM_amp;893.1;SPM_amp;MaximumLikelihoodPrinciple;SPM_amp;903.2;SPM_amp;_inline$chi^2$_inlineMethod;SPM_amp;1213.3;SPM_amp;CounterPhysics;SPM_amp;1323.4;SPM_amp;BubbleChamber;SPM_amp;139{tabular}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img7.gif">'; 
$key = q/{_inline}$y=leftlbrackarraylFGarrayrightrbrack,,hspace1emmu=leftlbrackarraylmu_fmu_garrayrightrbrack${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img345.gif">'; 
$key = q/{_inline}$Y^l_m${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1054.gif">'; 
$key = q/{_inline}$B=B_1+B_2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img69.gif">'; 
$key = q/{_inline}$mu_fmu_g${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img349.gif">'; 
$key = q/{_inline}$=sqrtmboxdiagonalelementsofmomentmatrix${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img190.gif">'; 
$key = q/{_inline}$4rightarrow6${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img457.gif">'; 
$key = q/{_inline}$x_1ldotsx_N${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1325.gif">'; 
$key = q/{_inline}$p_max=arrayccmaxxarray${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1497.gif">'; 
$key = q/{_inline}$P(SA)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img50.gif">'; 
$key = q/{_inline}$y=displaystylesum^N_i=1y_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img440.gif">'; 
$key = q/{_inline}$leftlanglex^nrightrangle=displaystyleintlimits^infty_-inftyx^np(x)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img155.gif">'; 
$key = q/{displaymath}L(tau)proptoexpleftlbrace-frac12tildesigma^2(tau-tau^*)^2rightrbrace{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img737.gif">'; 
$key = q/{_inline}$s(y|x)=delta(y-f(x))${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img142.gif">'; 
$key = q/{_inline}$bf$y$=TUnderline$x$${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img192.gif">'; 
$key = q/{_inline}$Re_k${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img10.gif">'; 
$key = q/{_inline}$tildep${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img947.gif">'; 
$key = q/{_inline}$=mu_f${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img353.gif">'; 
$key = q/{_inline}$ldots${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img698.gif">'; 
$key = q/{_inline}$Pleft(S_1+S_2+ldotsright)=Pleft(S_1right)+Pleft(S_2right)ldots+ldots${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img19.gif">'; 
$key = q/{_inline}$lambda_j${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1226.gif">'; 
$key = q/{_inline}$t_1ldotst_n${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img719.gif">'; 
$key = q/{_inline}$x_i=0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img925.gif">'; 
$key = q/{tabular}cclcr_inline$bullet$_inline;SPM_amp;change;SPM_amp;_inline$E_nrightarrowE_n+1$_inline;SPM_amp;chance;SPM_amp;_inline$lambda_ndt+o(dt)$_inline_inline$bullet$_inline;SPM_amp;;SPM_amp;_inline$E_nrightarrowE_n-1$_inline;SPM_amp;chance;SPM_amp;_inline$mu_ndt+o(dt)$_inline_inline$bullet$_inline;SPM_amp;Anyother;SPM_amp;change;SPM_amp;chance;SPM_amp;_inline$o(dt)$_inline{tabular}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img570.gif">'; 
$key = q/{_inline}$=sqrtxi_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img920.gif">'; 
$key = q/{_inline}$lambda_2=lambda_2p${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img489.gif">'; 
$key = q/{_inline}$+ldots${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1214.gif">'; 
$key = q/{_inline}$sigma^2=112${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1464.gif">'; 
$key = q/{_inline}$x_1ldotsx_n${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img188.gif">'; 
$key = q/{displaymath}bfMrightarrowbfM+QI{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1234.gif">'; 
$key = q/{_inline}$p^prime(x)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1519.gif">'; 
$key = q/{tabular}ll_inline$Psi(z)=sin(z2.1)$_inline;SPM_amp;_inline$vertzvert;SPM_lt;2.1pi$_inlinephantom_inline$Psi(z)$_inline_inline$=0$_inline;SPM_amp;_inline$vertzvertge2.1pi$_inline{tabular}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1404.gif">'; 
$key = q/{displaymath}displaystylesum^N_i=1frac(x_i-xi_i)^2sigma^2_i{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img878.gif">'; 
$key = q/{_inline}$O(sqrtN)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1129.gif">'; 
$key = q/{displaymath}w(F)=p(chi^2)fracd(chi^2)dF=1{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1269.gif">'; 
$key = q/{displaymath}p(x)=e^-x{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1486.gif">'; 
$key = q/{displaymath}Prm(heads)=lim_NrightarrowinftyfracN_hN=frac12{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img39.gif">'; 
$key = q/{_inline}$lambdadt+o(dt)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img546.gif">'; 
$key = q/{_inline}$p(x_1,ldotsx_n)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img167.gif">'; 
$key = q/{_inline}$r(x,y)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img127.gif">'; 
$key = q/{_inline}$displaystylesum^infty_k=0P(k,lambda)=1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img434.gif">'; 
$key = q/{displaymath}varphi(k)=sum_nk^nEfrac(ix)^nn!{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img267.gif">'; 
$key = q/{_inline}$[a,b]${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img11.gif">'; 
$key = q/{displaymath}leftlanglex_krightrangle=intlimitsotimes,dx_ihspace2emx_k,p(x_1ldotsx_n){displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img168.gif">'; 
$key = q/{_inline}$rho${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img304.gif">'; 
$key = q/{_inline}$p(x)dx=q(y)dy${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img120.gif">'; 
$key = q/{displaymath}1=(p+q)^n=sum^n_k=0b(k,n,p).{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img420.gif">'; 
$key = q/{_inline}$t(x|y)=r(x,y)q(y)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img133.gif">'; 
$key = q/{displaymath}I_j_1=I_j_2hspace2emj_1;SPM_gt;j_2{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1434.gif">'; 
$key = q/{_inline}$lambda_-1=0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img575.gif">'; 
$key = q/{displaymath}P_k(t+dt)=P_k(t)[1-lambdadt]+P_k-1(t)lambdadt+o(dt){displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img550.gif">'; 
$key = q/{_inline}$langlex^mrangle${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1035.gif">'; 
$key = q/{displaymath}arrayrlf=1;SPM_amp;hspace1emmboxeventpassesselectioncriteria=0;SPM_amp;hspace1emmboxeventfailscriterion.array{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img358.gif">'; 
$key = q/{_inline}$sigma${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img253.gif">'; 
$key = q/{_inline}$langlefrangle=planglegrangle${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img368.gif">'; 
$key = q/{_inline}$t(x|y)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img137.gif">'; 
$key = q/{_inline}$bfF=0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1155.gif">'; 
$key = q/{_inline}$[x,x+dx]${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img117.gif">'; 
$key = q/{_inline}$E_nrightarrowE_npm1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img592.gif">'; 
$key = q/{_inline}$x_1+x_2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img477.gif">'; 
$key = q/{_inline}$w_max${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1532.gif">'; 
$key = q/{displaymath}P_n(t)=e^-lambdamufracleft(fraclambdamuright)^nn!{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img584.gif">'; 
$key = q/{displaymath}A_1;SPM_gt;;SPM_gt;A_2{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1184.gif">'; 
$key = q/{_inline}$exists${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img561.gif">'; 
$key = q/{_inline}$T(XY)=t(x|y)dx${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img131.gif">'; 
$key = q/{_inline}$z_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img324.gif">'; 
$key = q/{_inline}$P(C)=P(A)P(B)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img58.gif">'; 
$key = q/{_inline}$t;SPM_gt;t_a${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1351.gif">'; 
$key = q/{_inline}$bullet${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1462.gif">'; 
$key = q/{_inline}$pml${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1315.gif">'; 
$key = q/{_inline}$x_2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img471.gif">'; 
$key = q/{_inline}$left(frac1taumboxhereright)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img725.gif">'; 
$key = q/{_inline}$i=1ldotsN${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img983.gif">'; 
$key = q/{displaymath}S(lambda)=frac1sqrtI(lambda)fracpartiallnLpartiallambda{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1303.gif">'; 
$key = q/{_inline}$(b-a)overlineI${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img331.gif">'; 
$key = q/{_inline}$displaystylesumf^2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img337.gif">'; 
$key = q/{_inline}$I_1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1432.gif">'; 
$key = q/{_inline}$I(lambda)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1304.gif">'; 
$key = q/{_inline}$L_3L_2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img790.gif">'; 
$key = q/{_inline}$}${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img973.gif">'; 
$key = q/{}psfigfigure=fig8.phys.ps,clip=true,width=3.25in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img667.gif">'; 
$key = q/{_inline}$1n${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img792.gif">'; 
$key = q/{displaymath}p(x)proptoexpleft(-frac(x-mu)^22sigma^2right){displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1367.gif">'; 
$key = q/{_inline}$trightarrowinfty${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img538.gif">'; 
$key = q/{displaymath}intlimits^+infty_-inftyexp(i,t,chi^2),p(chi^2),d(chi^2)=frac1sqrt1-2,i,t{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1262.gif">'; 
$key = q/{_inline}$sigma_x${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img163.gif">'; 
$key = q/{_inline}$B^-1=M${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img346.gif">'; 
$key = q/{}psfigfigure=fig9.phys.ps,clip=true,width=5.0in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img693.gif">'; 
$key = q/{_inline}$mboxbfM${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1207.gif">'; 
$key = q/{_inline}$(n_1,p)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img472.gif">'; 
$key = q/{_inline}$leftlangle(x-langlexrangle)^nrightrangle=displaystyleintlimits^+infty_-infty(x-langlexrangle)^n,p(x)dx${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img159.gif">'; 
$key = q/{_inline}$FG${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1075.gif">'; 
$key = q/{_inline}$F(x)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img103.gif">'; 
$key = q/{_inline}$Nmu${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img446.gif">'; 
$key = q/{displaymath}lambda_Lgerlambda_1mboxandlambda_L+1;SPM_lt;rlambda_1{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1221.gif">'; 
$key = q/{displaymath}fracdP_0(t)dt=-lambdaP_0(t)hspace1em:k=0{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img553.gif">'; 
$key = q/{}psfigfigure=fig24.phys.ps,clip=true,width=3.75in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1354.gif">'; 
$key = q/{displaymath}p(x)dx=d(F(x)){displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1481.gif">'; 
$key = q/{_inline}$M_m=${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1034.gif">'; 
$key = q/{_inline}$0leP(S)le1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img23.gif">'; 
$key = q/{}psfigfigure=fig13.phys.ps,clip=true,width=3.5in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1062.gif">'; 
$key = q/{_inline}$p^prime(x)=p(x)f(x)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1516.gif">'; 
$key = q/{_inline}$rightarrow0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1363.gif">'; 
$key = q/{_inline}$displaystyleintlimitsleftlbrackfracpartialpartiallambdalnP(x,lambda)rightrbrack^2P(x,lambda)dx${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1307.gif">'; 
$key = q/{displaymath}p(y)=frac1sqrt2pifracsqrtnsigmaexpleftlbrace-fracn(x-mu)^22sigma^2rightrbrace{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img315.gif">'; 
$key = q/{displaymath}F(x)=r{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1495.gif">'; 
$key = q/{_inline}$N-n_T${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img850.gif">'; 
$key = q/{displaymath}displaystyleintp(x),dx=1{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img319.gif">'; 
$key = q/{_inline}$sigma=1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1411.gif">'; 
$key = q/{displaymath}varphi_y(k)=leftlbrackvarphi_xleft(fracknright)rightrbrack^n{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img307.gif">'; 
$key = q/{_inline}$fracdisplaystyleintlimitsx,w(x)dxdisplaystyleintlimitsw(x)dx${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img408.gif">'; 
$key = q/{_inline}$sqrt-frac1L_2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img794.gif">'; 
$key = q/{displaymath}y^*_rmclever=left(frac1Nsum^N_i=1left(y^(i)right)^12right)^2{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1370.gif">'; 
$key = q/{_inline}$sigma^3${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img247.gif">'; 
$key = q/{displaymath}sum^N_i=1fracpartialpartialmulnpleft(fracleft(x^(i)-muright)sigmaright)=0{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1391.gif">'; 
$key = q/{_inline}$P(Y)=1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img17.gif">'; 
$key = q/{_inline}$Re_2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img147.gif">'; 
$key = q/{_inline}$y_1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img479.gif">'; 
$key = q/{_inline}$nlambda=Lambda${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img516.gif">'; 
$key = q/{displaymath}sigma^2=frac1nleftlangleleft(fracflanglegrangle-fracglanglefranglelanglegrangle^2right)^2rightrangle{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img804.gif">'; 
$key = q/{_inline}$f(x)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1066.gif">'; 
$key = q/{_inline}$nmu${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img502.gif">'; 
$key = q/{_inline}$x^(i)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1385.gif">'; 
$key = q/{_inline}$lambda_1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img492.gif">'; 
$key = q/{_inline}$b(k,n,p)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img500.gif">'; 
$key = q/{displaymath}p(F,G)proptoexpleftlbrace-fracn2(y-mu)^TB(y-mu)rightrbrace{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img344.gif">'; 
$key = q/{_inline}$frightarrowinfty${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1345.gif">'; 
$key = q/{_inline}$lambda_it${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img933.gif">'; 
$key = q/{_inline}$a_n_2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img405.gif">'; 
$key = q/{displaymath}K(k)=langlexrangleik-underbraceleft(leftlanglex^2rightrangle-langlexrangle^2right)_sigma^2frack^22{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img271.gif">'; 
$key = q/{_inline}$V_x=sigma^2_x${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img162.gif">'; 
$key = q/{_inline}$varphi_y${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img308.gif">'; 
$key = q/{displaymath}-lnL=-sum^N_i=1lnq_i{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1118.gif">'; 
$key = q/{_inline}$M_kl${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img186.gif">'; 
$key = q/{_inline}$r;SPM_gt;fracp(x)w_max${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1508.gif">'; 
$key = q/{_inline}$overlineI=frac1ndisplaystylesum^n_i=1fleft(x_iright)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img320.gif">'; 
$key = q/{_inline}$S_2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1130.gif">'; 
$key = q/{_inline}$(mboxbfa-mboxbfa^*)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img908.gif">'; 
$key = q/{_inline}$M_y${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img195.gif">'; 
$key = q/{_inline}$dx_j${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img980.gif">'; 
$key = q/{_inline}$beta)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img543.gif">'; 
$key = q/{displaymath}frac1lbrackNsigma^2rbrackbigvert_m.l.m.=intlimits^+1_-1fracdxpleft(fracpartialppartialaright)^2{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1043.gif">'; 
$key = q/{_inline}$(sqrtN)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1064.gif">'; 
$key = q/{displaymath}y^*_Am=frac1Nsum^N_i=1y^(i){displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1371.gif">'; 
$key = q/{_inline}$g(t)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img227.gif">'; 
$key = q/{_inline}$Psi${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1393.gif">'; 
$key = q/{_inline}$R(j)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1461.gif">'; 
$key = q/{_inline}$e_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1090.gif">'; 
$key = q/{_inline}$x_k-x_k-1=deltax${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1492.gif">'; 
$key = q/{_inline}$displaystylesum^infty_N=0Pr(Nmboxtakesgivenvalue)timesPrleft(displaystylesum^N_i=1y_i(Nmboxfixedhas$r$events)right)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img445.gif">'; 
$key = q/{_inline}$Pleft(S_2right)ge0RightarrowPleft(S_1right)=P(S)le1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img28.gif">'; 
$key = q/{displaymath}chi^2left(bf_inline$beta$_inline_0+Deltabetaright);SPM_gt;chi^2left(bf_inline$beta$_inline_0right){displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1237.gif">'; 
$key = q/{_inline}$y=displaystylesum^N_gamma_i=1y_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img464.gif">'; 
$key = q/{_inline}$n_k${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img997.gif">'; 
$key = q/{displaymath}mu^*_,rmtrim=fracdisplaystylesum^N(1-p)_i=pN+1x^(i)N(1-2p){displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1375.gif">'; 
$key = q/{_inline}$F(chi^2)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1266.gif">'; 
$key = q/{_inline}$u_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1468.gif">'; 
$key = q/{_inline}$rhopropton^13${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img305.gif">'; 
$key = q/{_inline}$sigma^2_rmphysis${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img812.gif">'; 
$key = q/{_inline}$phi(betaT)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img655.gif">'; 
$key = q/{_inline}$xleftrightarrowy${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img123.gif">'; 
$key = q/{_inline}$[0,1]${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1506.gif">'; 
$key = q/{displaymath}mboxbfa^*=mboxbfM^-1mboxbfb{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img900.gif">'; 
$key = q/{displaymath}w=intlimits^x_-inftyp(x)dx{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1483.gif">'; 
$key = q/{_inline}$y_1leyley_2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1074.gif">'; 
$key = q/{tabular}rclcr_inline$Psi(z)$_inline;SPM_amp;=;SPM_amp;_inline$z$_inline;SPM_amp;for;SPM_amp;_inline$|z|lez_c$_inlineand_inline$Psi(z)$_inline;SPM_amp;=;SPM_amp;_inline$z_c$_inline;SPM_amp;for;SPM_amp;_inline$z;SPM_gt;z_c$_inline;SPM_amp;=;SPM_amp;_inline$-z_c$_inline;SPM_amp;for;SPM_amp;_inline$z;SPM_gt;-z_c$_inline{tabular}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1400.gif">'; 
$key = q/{displaymath}frac1sqrtN,sqrtfrac1Nsum^N_i=1f^2(x_i)-left(frac1Nsum^N_i=1f(x_i)right)^2{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1025.gif">'; 
$key = q/{_inline}$1mu${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img581.gif">'; 
$key = q/{_inline}$vertT${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img649.gif">'; 
$key = q/{_inline}$Lproptoexpleftlbrace-frac12(rmx-xi)^TM(rmx-xi)rightrbrace${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img860.gif">'; 
$key = q/{_inline}$4lambda${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img462.gif">'; 
$key = q/{_inline}$N_h${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img38.gif">'; 
$key = q/{_inline}$bulletn_rm,tot${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img54.gif">'; 
$key = q/{_inline}$p(x)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1373.gif">'; 
$key = q/{_inline}$langleyrangle=tau_0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img730.gif">'; 
$key = q/{_inline}$P_l${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img207.gif">'; 
$key = q/{_inline}$L_1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img778.gif">'; 
$key = q/{_inline}$beta=displaystyleintlimits_R-rP^(1)_Y(y)dy${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1333.gif">'; 
$key = q/{_inline}$S(YX)=s(y|x)dy${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img134.gif">'; 
$key = q/{_inline}$P(A)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img98.gif">'; 
$key = q/{tabular}lll_inline$x_i$_inline;SPM_amp;0;SPM_amp;_inline$=F(x_1)$_inline_inline$x_1+deltax$_inline;SPM_amp;_inline$p(x_1)$_inline;SPM_amp;_inline$=F(x_1+deltax)$_inline_inline$x_1+2deltax$_inline;SPM_amp;_inline$p(x_1)+p(x_2)$_inline;SPM_amp;_inline$=F(x_1+2deltax)$_inline_inline$vdots$_inline_inline$x_m+1$_inline;SPM_amp;_inline$displaystylesum^m_i=1p(x_i)$_inline;SPM_amp;=1ifnormalized_inline$=F(x_m+1)$_inline{tabular}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1493.gif">'; 
$key = q/{_inline}$C(chi^2)=1-F(chi^2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1270.gif">'; 
$key = q/{_inline}$f^prime(x_1ldotsx_n)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1081.gif">'; 
$key = q/{}psfigfigure=fig21.phys.ps,clip=true,width=3.25in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1279.gif">'; 
$key = q/{_inline}$varphi${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1059.gif">'; 
$key = q/{_inline}$V_x${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img164.gif">'; 
$key = q/{_inline}$a_n${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img392.gif">'; 
$key = q/{_inline}$F(infty)=1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img102.gif">'; 
$key = q/{_inline}$P(S)=12${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img40.gif">'; 
$key = q/{displaymath}w(h)=intlimits^+infty_-inftyintlimits^+infty_-inftydelta(h-x-y),p(x),q(y)dx,dy{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img264.gif">'; 
$key = q/{_inline}$P(x_ivertT)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img724.gif">'; 
$key = q/{_inline}$pi${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1438.gif">'; 
$key = q/{_inline}$(1-2,i,t)^-frack2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1264.gif">'; 
$key = q/{_inline}$left(arraylnkarrayright)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img416.gif">'; 
$key = q/{_inline}$y=x^2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1369.gif">'; 
$key = q/{_inline}$r=0.1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1222.gif">'; 
$key = q/{displaymath}fracPleft(B_1Aright)Pleft(B_2Aright)=fracPleft(AB_1right)Pleft(B_1right)Pleft(AB_2right)Pleft(B_2right){displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img97.gif">'; 
$key = q/{_inline}$displaystylesumf${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img338.gif">'; 
$key = q/{_inline}$sigma^2_rmstatistical${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img809.gif">'; 
$key = q/{_inline}$displaystylesum^t_i=1y_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img534.gif">'; 
$key = q/{_inline}$pm(x-t)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1253.gif">'; 
$key = q/{_inline}$tau${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img735.gif">'; 
$key = q/{_inline}$k=1ldotsK${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img989.gif">'; 
$key = q/{}psfigfigure=fig22.phys.ps,clip=true,width=3.25in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1283.gif">'; 
$key = q/{_inline}$infty${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1478.gif">'; 
$key = q/{_inline}$geq0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img174.gif">'; 
$key = q/{displaymath}p(x)=frac12(1+ax)hspace2em-1lexle1{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1032.gif">'; 
$key = q/{_inline}$p=frac120.50=frac11000${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img435.gif">'; 
$key = q/{_inline}$N=1!${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1031.gif">'; 
$key = q/{_inline}$chi^2;SPM_gt;;SPM_gt;(n-m)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1280.gif">'; 
$key = q/{_inline}$mu_0=0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img574.gif">'; 
$key = q/{_inline}$O(1n)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img784.gif">'; 
$key = q/{_inline}$=displaystyleintlimits_rP^(0)_Y(y)dy${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1330.gif">'; 
$key = q/{_inline}$f^prime${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1084.gif">'; 
$key = q/{_inline}$tildesigma${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img738.gif">'; 
$key = q/{displaymath}frac1lbrackNsigma^2rbrackbigvert_m.l.m.=inftymboxwhena=pm1.{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1047.gif">'; 
$key = q/{_inline}$^*${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img886.gif">'; 
$key = q/{_inline}$mu^*${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1376.gif">'; 
$key = q/{_inline}$O(N)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1131.gif">'; 
$key = q/{_inline}$-frac12(mboxbfa-mboxbfa^*)^TmboxbfM(mboxbfa-mboxbfa^*)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img909.gif">'; 
$key = q/{_inline}$b(k,1,p)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img495.gif">'; 
$key = q/{_inline}$f_2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img458.gif">'; 
$key = q/{_inline}$p_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img976.gif">'; 
$key = q/{_inline}$tau_0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img718.gif">'; 
$key = q/{}psfigfigure=fig15.phys.ps,clip=true,width=4.5in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1177.gif">'; 
$key = q/{}psfigfigure=fig28b.phys.ps,clip=true,width=4.0in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1453.gif">'; 
$key = q/{_inline}$n_1=lambda_2p${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img488.gif">'; 
$key = q/{displaymath}frac1nsum^n_i=1f^2left(x_iright){displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img336.gif">'; 
$key = q/{}psfigfigure=fig18.phys.ps,clip=true,width=4.5in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1208.gif">'; 
$key = q/{_inline}$frac1Nsigma^2bigvert_1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1046.gif">'; 
$key = q/{_inline}$x_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img251.gif">'; 
$key = q/{_inline}$Lambda${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1421.gif">'; 
$key = q/{_inline}$div${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1414.gif">'; 
$key = q/{_inline}$frac(x-mu)sigma${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1405.gif">'; 
$key = q/{_inline}$n_irightarrowinfty${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img490.gif">'; 
$key = q/{_inline}$Pleft(S_1-S_1,S_2right)lePleft(S_1right)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img35.gif">'; 
$key = q/{_inline}$x_i=1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img497.gif">'; 
$key = q/{displaymath}F(x)=Phi(x)=frac1sqrt2pisigmadisplaystyleintlimits^x_-inftydyexpleftlbrack-frac(y-mu)^22sigma^2rightrbrack{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img112.gif">'; 
$key = q/{_inline}$lambda_1+lambda_2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img485.gif">'; 
$key = q/{_inline}$I_j-p${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1447.gif">'; 
$key = q/{_inline}$E_n-1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img568.gif">'; 
$key = q/{_inline}$P(S)ge0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img24.gif">'; 
$key = q/{displaymath}sigma^2=sum^N_i=1omega_i^2{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1102.gif">'; 
$key = q/{_inline}$qbf$q$${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img453.gif">'; 
$key = q/{displaymath}lambda_1gelambda_2geldotsgelambda_nge0{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1216.gif">'; 
$key = q/{_inline}$(n_1+n_2,p)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img478.gif">'; 
$key = q/{_inline}$h(x,y)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img148.gif">'; 
$key = q/{_inline}$sigma=sqrtfrac1nsigma^2_f${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img354.gif">'; 
$key = q/{_inline}$2^p-1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1448.gif">'; 
$key = q/{_inline}$[y,y+dy]${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img119.gif">'; 
$key = q/{}psfigfigure=fig28.phys.ps,clip=true,width=4.5in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1419.gif">'; 
$key = q/{_inline}$(n)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img744.gif">'; 
$key = q/{_inline}$z_i=fleft(x_iright)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img323.gif">'; 
$key = q/{_inline}$lambda${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1302.gif">'; 
$key = q/{_inline}$tildep(k)=fraclambda_kLambda${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img946.gif">'; 
$key = q/{_inline}$y=f(x)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img114.gif">'; 
$key = q/{_inline}$sqrt2k${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1248.gif">'; 
$key = q/{_inline}$f_2;SPM_gt;0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img459.gif">'; 
$key = q/{_inline}$xi_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img855.gif">'; 
$key = q/{_inline}$displaystylesum^N_i=1v_i^2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img841.gif">'; 
$key = q/{_inline}$displaystylesumpropton^12${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img306.gif">'; 
$key = q/{_inline}$g_1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1475.gif">'; 
$key = q/{displaymath}s(y|x)=fracr(x,y)p(x){displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img135.gif">'; 
$key = q/{_inline}$I_2ldots${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1433.gif">'; 
$key = q/{_inline}$(a,b)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img12.gif">'; 
$key = q/{_inline}$Nrightarrowinfty${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1364.gif">'; 
$key = q/{displaymath}langlexrangle=fracdisplaystylesum^N_i=1w_i,x_i=S_3displaystylesum^N_i=1w_i=S_1{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img409.gif">'; 
$key = q/{_inline}$varphi(k)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img266.gif">'; 
$key = q/{_inline}$p(x,mu)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1388.gif">'; 
$key = q/{_inline}$mu_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1104.gif">'; 
$key = q/{_inline}$y=frac1ndisplaystylesum^n_i=1t_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img729.gif">'; 
$key = q/{_inline}$mu_n(t)dt${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img569.gif">'; 
$key = q/{_inline}$S(lambda)=mp1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1312.gif">'; 
$key = q/{_inline}$lim_nrightarrowinftyrhoSigmarightarrow0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img297.gif">'; 
$key = q/{_inline}$rho_1-1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img865.gif">'; 
$key = q/{_inline}$H_0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1319.gif">'; 
$key = q/{_inline}$M_m${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1036.gif">'; 
$key = q/{_inline}$sigma_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1287.gif">'; 
$key = q/{}psfigfigure=fig25b.phys.ps,clip=true,width=5.0in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1415.gif">'; 
$key = q/{_inline}$S_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img20.gif">'; 
$key = q/{_inline}$nrightarrowinfty${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img314.gif">'; 
$key = q/{tabular}rcll_inline$C(chi^2)=1$_inline;SPM_amp;is;SPM_amp;_inline$chi^2=0$_inline;SPM_amp;``good''_inline$=0$_inline;SPM_amp;is;SPM_amp;_inline$chi^2=infty$_inline;SPM_amp;``bad''or``lowconfidence''{tabular}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1271.gif">'; 
$key = q/{_inline}$Lambda=displaystylesum^M_i=1lambda_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img941.gif">'; 
$key = q/{_inline}$fracsigmasqrtn${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img666.gif">'; 
$key = q/{_inline}$bulletn(A)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img55.gif">'; 
$key = q/{_inline}$sigma_y${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img236.gif">'; 
$key = q/{_inline}$a_1sigma_1=0Rightarrowsigma_y=tildesigma_y${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img240.gif">'; 
$key = q/{_inline}$sqrtLambda${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img525.gif">'; 
$key = q/{_inline}$rho_kl=0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img178.gif">'; 
$key = q/{_inline}$t;SPM_lt;t_a${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1350.gif">'; 
$key = q/{_inline}$1(l)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1317.gif">'; 
$key = q/{_inline}$frac1nlanglegrangle${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img810.gif">'; 
$key = q/{_inline}$oplus${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1445.gif">'; 
$key = q/{_inline}$langleg^2rangle=langlegrangle${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img376.gif">'; 
$key = q/{displaymath}lambda_k=int_,mboxsmallbinfork'thgroup,p,dx,{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img991.gif">'; 
$key = q/{_inline}$P(S)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img48.gif">'; 
$key = q/{_inline}$[x_1,x_2]${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1512.gif">'; 
$key = q/{displaymath}xi_i=sum^n_T_m=1C_ima_m{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img876.gif">'; 
$key = q/{displaymath}a^*_m=(m+2)sum^N_i=1fracx^m_iN{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1038.gif">'; 
$key = q/{displaymath}lnL=mboxconst.+underbracelbraceNln(tLambda)-tLambdarbrace_(a)+underbracesum^M_i=1n_iln(lambdaLambda)_(b){displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img956.gif">'; 
$key = q/{_inline}$w_rmmax${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1501.gif">'; 
$key = q/{_inline}$w_i(i=1ldotsN)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img406.gif">'; 
$key = q/{_inline}$I_j_1-1=I_j_2-1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1436.gif">'; 
$key = q/{_inline}$sigma_1=sigma_2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img214.gif">'; 
$key = q/{_inline}$j=L+1ldotsn${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1219.gif">'; 
$key = q/{_inline}$f_2=0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img463.gif">'; 
$key = q/{_inline}$sigma=mboxmeanvertx^(i)-muvert${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1408.gif">'; 
$key = q/{_inline}$kge3${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1180.gif">'; 
$key = q/{_inline}$y_2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img480.gif">'; 
$key = q/{_inline}$mu_i=fraclambda_iLambda${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img953.gif">'; 
$key = q/{_inline}$displaystylesum^t_i=1lambda_i=pt${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img535.gif">'; 
$key = q/{_inline}$langlesigma^2_rmphysicsrangle${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img814.gif">'; 
$key = q/{_inline}$E_j${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img596.gif">'; 
$key = q/{displaymath}fraclambda_rmmaxlambda_rmmin=fraclambda_1lambda_nsim10^7mboxfornsim30{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1227.gif">'; 
$key = q/{displaymath}mboxbfM_,kl=intlimitsotimes,dx_ileftlbrackmboxbfx_,k-leftlanglemboxbfx_,krightranglerightrbrackleftlbrackmboxbfx_,l-leftlanglemboxbfx_,lrightranglerightrbrackpleft(x_1ldotsx_nright){displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img170.gif">'; 
$key = q/{_inline}$lambda_2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img493.gif">'; 
$key = q/{displaymath}P_k(t)=e^-lambdatfrac(lambdat)^kk!{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img555.gif">'; 
$key = q/{_inline}$I_0=${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1451.gif">'; 
$key = q/{displaymath}I(lambda)=NintlimitsleftlbrackfracpartialpartiallambdalnP(x,lambda)rightrbrack^2P(x,lambda)dx{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1306.gif">'; 
$key = q/{_inline}$q=1920${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img422.gif">'; 
$key = q/{_inline}${${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img970.gif">'; 
$key = q/{_inline}$1^-${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img867.gif">'; 
$key = q/{_inline}$p_jkdt${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img595.gif">'; 
$key = q/{displaymath}intlimits^b_af^2(x)p(x)dx=leftlanglef^2(x)rightrangle{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img335.gif">'; 
$key = q/{_inline}$y_i(=0mboxno,=1mboxonecall)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img532.gif">'; 
$key = q/{displaymath}P(BA)=fracP(B)P(AB)P(A){displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img66.gif">'; 
$key = q/{_inline}$r^2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1259.gif">'; 
$key = q/{_inline}$y_k,M_kl,y_l${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img172.gif">'; 
$key = q/{_inline}$fracn!(n-k)!=n(n-1)ldots(n-k+1)rightarrown^k${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img430.gif">'; 
$key = q/{_inline}$chi^2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1316.gif">'; 
$key = q/{_inline}$Oleft(frac1nright)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img775.gif">'; 
$key = q/{_inline}$p(x)=0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1484.gif">'; 
$key = q/{_inline}$L=displaystyleprod^N_j=1tildep(C_j)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img951.gif">'; 
$key = q/{_inline}$sqrtx_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img923.gif">'; 
$key = q/{_inline}$f(x)dx=d(F(x))${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1511.gif">'; 
$key = q/{displaymath}p(x)=frac12leftlbrackdelta(x)+delta(x-1)rightrbrack{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img108.gif">'; 
$key = q/{displaymath}tildesigma_y=sqrta_1^2sigma_1^2+a_2^2sigma_2^2{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img235.gif">'; 
$key = q/{_inline}$S(lambda)=pm1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1314.gif">'; 
$key = q/{_inline}$i:x_i=0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img496.gif">'; 
$key = q/{_inline}$(x^(i)-mu)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1399.gif">'; 
$key = q/{displaymath}P_k(t)=e^-ptfrac(pt)^kk!{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img536.gif">'; 
$key = q/{_inline}$chi^2=chi^2_0+mboxlinearterms+lambda_1left(beta_1-beta_01right)^2+lambda_2left(beta_2-beta_01right)^2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1213.gif">'; 
$key = q/{_inline}$y=x_1ldots+x_n${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img515.gif">'; 
$key = q/{_inline}$rlefracp(x)w_max${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1510.gif">'; 
$key = q/{_inline}$p(x)dx${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img118.gif">'; 
$key = q/{}psfigfigure=fig10.phys.ps,clip=true,width=5.5in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img734.gif">'; 
$key = q/{}psfigfigure=fig11.phys.ps,clip=true,width=5.5in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img870.gif">'; 
$key = q/{_inline}$sqrtNlanglegrangle=N_rmhist-${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img378.gif">'; 
$key = q/{}psfigfigure=fig12.phys.ps,clip=true,width=5.5in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img930.gif">'; 
$key = q/{displaymath}=sum_ifrac(partialxi_ipartiala_m)(partialxi_ipartiala_l)sigma^2_i{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img893.gif">'; 
$key = q/{displaymath}frac1n,T,r,bfM=frac1n,sum^n_j=1lambda_j{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1238.gif">'; 
$key = q/{_inline}$pm${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img189.gif">'; 
$key = q/{_inline}$overlineIrightarrowfracI(b-a)pmfracsigmasqrtn${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img330.gif">'; 
$key = q/{_inline}$I_j_1-j_2=I_0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1437.gif">'; 
$key = q/{displaymath}w(x)=1-e^-x{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1487.gif">'; 
$key = q/{_inline}$z_1=-z_2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img215.gif">'; 
$key = q/{_inline}$S_1,2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1126.gif">'; 
$key = q/{_inline}$M_jk${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1143.gif">'; 
$key = q/{_inline}$sigma^2_rmphysics${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img815.gif">'; 
$key = q/{displaymath}mu_i=fracn_iN{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img955.gif">'; 
$key = q/{_inline}$inej${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img22.gif">'; 
$key = q/{_inline}$mboxbfa^*${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img902.gif">'; 
$key = q/{_inline}$x_i=k${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img475.gif">'; 
$key = q/{_inline}$sigmasqrtN${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img384.gif">'; 
$key = q/{displaymath}r(x,y)=deltaleftlbracky-f(x)rightrbrackp(x).{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img145.gif">'; 
$key = q/{_inline}$(n_2,p)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img473.gif">'; 
$key = q/{displaymath}frac1Nsum^N_i=1f(x_i)rightarrowmu{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1006.gif">'; 
$key = q/{_inline}$mu_0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1027.gif">'; 
$key = q/{_inline}$[p(x)]${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1498.gif">'; 
$key = q/{}psfigfigure=fig23.phys.ps,clip=true,width=3.0in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1286.gif">'; 
$key = q/{_inline}$N_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img44.gif">'; 
$key = q/{_inline}$Pleft(S+1+S_2right)lePleft(S_1right)+P(S_2)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img29.gif">'; 
$key = q/{_inline}$0;SPM_lt;t_a;SPM_lt;left(mu_1-mu_0right)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1349.gif">'; 
$key = q/{displaymath}lim_NrightarrowinftyfracN_hN=frac12{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img37.gif">'; 
$key = q/{_inline}$r(x,y)dxdy${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img129.gif">'; 
$key = q/{_inline}$xleq1(.5leqxleq1mboxintheexperiment)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img218.gif">'; 
$key = q/{_inline}$mu_n=nmu${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img579.gif">'; 
$key = q/{_inline}$L_2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img779.gif">'; 
$key = q/{}psfigfigure=fig26.phys.ps,clip=true,width=5.5in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1401.gif">'; 
$key = q/{_inline}$sigma_0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img616.gif">'; 
$key = q/{displaymath}p(t)dt=frac1tauexpleft(-fracttauright)dt{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img720.gif">'; 
$key = q/{}psfigfigure=fig2.phys.ps,clip=true,width=4.5in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img43.gif">'; 
$key = q/{_inline}$prightarrow0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img491.gif">'; 
$key = q/{_inline}$sigmasqrtn${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img671.gif">'; 
$key = q/{}psfigfigure=fig6.phys.ps,clip=true,width=4.5in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img223.gif">'; 
$key = q/{displaymath}0leqsigma_yleqsqrtntildesigma_y{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img241.gif">'; 
$key = q/{_inline}$N_gamma=${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img466.gif">'; 
$key = q/{_inline}$g(x)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img341.gif">'; 
$key = q/{_inline}$displaystylesum^M_i=1mu_i=1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img954.gif">'; 
$key = q/{_inline}$n_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img960.gif">'; 
$key = q/{_inline}$o(dt)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img548.gif">'; 
$key = q/{_inline}$I_j_1+1=I_j_2+1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1435.gif">'; 
$key = q/{_inline}$p(y)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1078.gif">'; 
$key = q/{_inline}$langleQrangle${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1525.gif">'; 
$key = q/{_inline}$v_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img842.gif">'; 
$key = q/{_inline}$P(B)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img89.gif">'; 
$key = q/{_inline}$P(AB)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img80.gif">'; 
$key = q/{_inline}$xrightarrowx+mu${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img272.gif">'; 
$key = q/{_inline}$(b-a)fracsigmasqrtn${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img332.gif">'; 
$key = q/{_inline}$sigma^2_y=a_1^2sigma_1^2+a_2^2sigma_2^2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img232.gif">'; 
$key = q/{_inline}$xilex${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img100.gif">'; 
$key = q/{_inline}$YinRe_k${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img42.gif">'; 
$key = q/{_inline}$langlegrangle${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img808.gif">'; 
$key = q/{_inline}$x_2ldotsx_n${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img600.gif">'; 
$key = q/{_inline}$y=a_1x_1+a_2x_2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img231.gif">'; 
$key = q/{_inline}$ikmu${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img273.gif">'; 
$key = q/{_inline}$Gamma(12)=sqrtpi${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1252.gif">'; 
$key = q/{_inline}$C(chi^2)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1285.gif">'; 
$key = q/{_inline}$b(k,t,p)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img537.gif">'; 
$key = q/{_inline}$langlexrangle=displaystyleintlimits^+infty_-inftyxp(x)dx${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img154.gif">'; 
$key = q/{_inline}$leftlangleleft(fracpartialpartiallambdalnLright)^2rightrangle${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1305.gif">'; 
$key = q/{_inline}$y=x-mu${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img246.gif">'; 
$key = q/{_inline}$(x_1ldotsx_N)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1324.gif">'; 
$key = q/{_inline}$P(BA)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img96.gif">'; 
$key = q/{_inline}$langleyrangle${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img254.gif">'; 
$key = q/{_inline}$frack^2n${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img313.gif">'; 
$key = q/{_inline}$(10^6)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img1241.gif">'; 
$key = q/{displaymath}fracpartialpartialmulnL=0{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1390.gif">'; 
$key = q/{_inline}$N_1+N_2+N_3+N_4=N${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img47.gif">'; 

1;

