Prove that the sum of n independently and identically distributed (IID) exponential random variables with parameter has a gamma distribution and identify the parameters of the gamma distribution.
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Show that the sum of independent identically distributed exponential random variables has a gamma distribution.
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Show that $\prod_{i=1}^{n} X_{i}$ and $\sum_{i=1}^{n} X_{i}$ are sufficient statistics for the gamma distribution.
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