Question: Let X be a geometric variable with parameter p(0,1). Given X=k, we have that Y is a Gamma variable with parameters k and >0 (i.e.,

Let X be a geometric variable with parameter p(0,1). Given X=k, we have that Y is a Gamma variable with parameters k and >0 (i.e., given X=k, Y is the sum of k independent exponential variables with rate ). Compute P(X=k|Y=y) for y >0,k1. Please simplify your answer as much as possible (i.e., do not leave integrals or summations in your answer)

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