## Distribution of average of exponentially distributed [closed]

We independently choose n r.v.s from an exponential distribution with parameter lambda. What is the distribution of the average of these n variables? (in the context of finding the distribution of the mle)

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 The answer is: Gamma. However, this question does not fit in MO. – Didier Piau Feb 12 2011 at 16:57 Presumably for large $n$ the normal approximation works well... – Igor Rivin Feb 12 2011 at 17:01