2 Let X1,X2, ,Xn be n independent exponential random variables with the identical mean 1 Use moment generating functions to show that the distribution of X1 X2 Xn is gamma with parameters n and ...

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2. Let X1,X2, . . . ,Xn be n independent exponential random variables with the identical mean...

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2. Let X1,X2, . . . ,Xn be n independent exponential random variables with the identical mean 1/λ. Use moment-generating functions to show that the distribution of X1+X2+

· · · + Xn is gamma with parameters n and λ.

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