Question: Problem 3.13 The random variable Y has a geometric distribution P(Y = j) = pqj1, j = 1,..., ; 0 a) = qa. (b) Show

Problem 3.13 The random variable Y has a geometric distribution P(Y = j) = pqj−1, j = 1,..., ; 0

a) = qa.

(b) Show that P(Y >a + b|Y >b) = P(Y >a).

(c) Show that P(Y is odd )=1/(1 + q).

(d) Compute the probability function of (−1)Y . Hint for (c): Use Equation 3.6 with a suitable choice for r.

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