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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

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Distribution of the standard deviation of normal variates

What is the distribution of the standard deviation of $n$ normal variates? That is, if $X_1,...,X_n$ are i.i.d. normal random variables with mean $\mu$ and s.d. $\sigma$ and $M=\sum X_i/n$, then what …