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    Jointly Distributed Random Variables : Gamma and Exponential Distributions

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    If X1, X2,...Xn are all independent Expo(λ), and Sn=Σ i=1..n Xi, then Sn≈Gamma (n,λ). Show that this is true when n=2.

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    (This problem is from the chapter of Jointly Distributed Random Variables.)

    Before I prove this question, I would like to recall the Exponential random variable and Gamma distribution.

    A random variable is said to have a gamma distribution with parameters if its density function is

    Solution Summary

    Gamma and Exponential Distributions with regard to Jointly Distributed Random Variables are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.