Question: Let U be a uniform variable on [0, 1] and let N be an independent Poisson variable with mean 1. Given U = u and

Let U be a uniform variable on [0, 1] and let N be an independent Poisson variable with mean 1. Given U = u and N = n, we toss a p-coin (with p = u) for n times and let S be the number of heads obtained.

(a) Find P(S = 0).

(b) Find the conditional density of U given S = 0.

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