Problem 2. Let X be a geometric variable with parameter p E (0. 1). Given X = k, we have that Y is a Gamma variable with parameters k and A > 0 (i.e., given X = k, Y is the sum of k independent exponential variables with rate A). Compute lP(X = k | Y = y) for y > 0.1: 2 1. Please simplify your answer as much as possible (i.e., do not leave integrals or summations in your answer)