Question: 2. Consider the same setting as in Exercise 1, except now P is assumed here to have the uniform(0, 1) distribution. (a) Use the principle

2. Consider the same setting as in Exercise 1, except now P is assumed here to have the uniform(0, 1) distribution.

(a) Use the principle of hierarchical modeling to specify the joint density of fP,Y(p, y) of (P,Y) as the product of the conditional PMF of Y given P = p times the marginal PDF of P.

(b) Find the marginal PMF of Y. (Hint. The marginal PDF of Y is still given by integrating fP,Y(p, y) over p. You may use 9 1 0

/nk0 pk(1 − p)n−k dp = 1 n+1 for k = 0, . . . , n.)

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