Let X be a random variable with geometric(p) distribution on {0, 1,

2, . . . }. Given X = x, Y has negative binomial (x, p) distribution on {0, 1, 2, . . . }.

1. (5pt) For x a fixed integer, what is P(Y = x|X = x)?

2. (5pt) What is P(X = Y )? (You can leave this result as an unsimplified sum.)

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