Determination of Lifetime Example of Maximum Likelihood---I

• All books give the example of determining the lifetime of a particle from the observation of decay times of n decays.

• The probability distribution for decay problem is Poisson:

  

• Now, dt is meaningless---it is independent of and only affects normalization of likelihood.

  The unknown , terms in Equation (14) made this arbitrary anyway.

• We must, however, keep terms in normalization that depend on parameters to be determined.

• The likelihood of n decays is:

  

  where we lazily convert into an = sign.