The probability generating function of the discrete nonnegative integer valued random variable having probability mass function p j , j 0, is defined by Let be a geometric random variable with parameter p 1 s, where 0 s 1 Suppose that is independent of X, and show that (s) P X Y co $(s) E s 2 P,si j 0

Question: The probability generating function of the discrete nonnegative integer valued random variable having probability mass function p j , j 0, is defined by

The probability generating function of the discrete nonnegative integer valued random variable having probability mass function p_j, j ≥ 0, is defined by

co $(s) = E[s*] = 2 P,si j = 0

Let be a geometric random variable with parameter p = 1 - s, where 0

ϕ(s) = P{X

co $(s) = E[s*] = 2 P,si j = 0

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