Suppose X₁, X2, ..., Xn are i.i.d expoential random variables with parameter A. Let Z = EX₁. Show that Z is the gamma distribution with parameter (A, n) (Hint: By induc- tion, it suffices to check that if X is a gamma distribution with parameter (A, n) and Y is the gamma distribution with parameter (A, n − 1) then X + Y is a gamma distribution with parameter (A, n).)

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