Question: 1. Let X have probability generating function GX (s) and let un = P(X > n). Show that the generating function U(s) of the sequence

1. Let X have probability generating function GX (s) and let un = P(X > n). Show that the generating function U(s) of the sequence u0, u1, . . . satisfies

(1 − s)U(s) = 1 − GX (s), whenever the series defining these generating functions converge.

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