Where do random numbers come from really?

Monte Carlo.

Uniformly distributed random variates Xi = remainder(aXi-1 / m)

For example, a= 75 m= 231 -1

Given two Xj Xk such uniform random variates,

Normally distributed random variates can be made

(with mX = 0 sX = 1)

Xi = sqrt(-2log(Xj)) cos(2pXk) (NR, Press et al. p. 279-89)

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