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Intuitively, random numbers come from large physical systems whose size implies that different atoms act (decay) independently, e.g. observed time of decay of radioactive particle is a random number.
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Computers generate "pseudo random numbers"
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For instance, with the sequence
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xn+1 = (axn + c) mod m
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where certain choices of a, c, m are good.
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See Knuth1 or Numerical Recipes2.
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1) Knuth, D.E., "Seminumerical Algorithms "Vol. 2, The Art of Computer Programming, Addison-Wesley Publishing Co.1969
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2) Flannery,B.P., Press,W.H., Teukolsky,S.A., Vetterling,W.T., "Numerical Recipes in Fortran", The Art of Scientific Computing, Cambridge University Press 1992
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Secs 132.4