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Institute of Mathematics
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Central limit theorem

For i.i.d. distributed random variables X1,X2,.. with common expected value µ and variance σ2strives

for n→∞ against the standard normal distribution N(0,1).

For illustration purposes, the Xi are replaced by simulated random numbers for the selected distribution. The relative frequencies of the Yn values determined for this are displayed; they quickly approach the density of N(0,1).