1. Suppose that X is a random variable taking non-negative integer values, and l

Question

1. Suppose that X is a random variable taking non-negative integer values, and let GX(z) be the probability generating function for X.

a) Find the probability generating function for the random variable Y = X + 1.

b) Let bn = P(X < n). Find a closed-form generating function for {bn} in terms of Gx(z).

2. Consider a sequence of independent rolls of a die, and let X be a random variable that records the number of consecutive trials that all have the same value as the initial roll. Let Cn be P (X >= n).

a) Find a formula for Cn.

b)

Find a closed-form expression for C(z).

Explanation / Answer

y=x+1 it will have positive integers for x>-1

so p(y) =p(x>-1)/p(x belongs to I)

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