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Assume that iid exponential random variables {X,, }0_ are independent of a geometric random variable N with pmf py (k) = (1 - a)*-la for

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Assume that iid exponential random variables {X,, }0_ are independent of a geometric random variable N with pmf py (k) = (1 - a)*-la for k E {1,2, ...}. Obtain the distribution of the random sum SN = >-1 X;. (Hint: use MGF)

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