Question: Problem 3. There is a slot machine such that each time you play with it, you win with probability q = 0.25 and lose with

Problem 3. There is a slot machine such that each time you play with it, you win with probability q = 0.25 and lose with probability 1 -q = 0.75 independent of prior times. Suppose that you play with the machine for four times. Let . X = #of losses, and . Y = # of losses before the first win. Further, let's assume Y = 4 if you lose all the four tries. Find the (marginal) PMF of X, Y and joint PMF of X, Y

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