Question: 8.5.2 Let X be a nonnegative integer-valuedrandom variable. The function gx (s) = E s X , defined for Is1 5 1, is called a

8.5.2 Let X be a nonnegative integer-valuedrandom variable. The function gx (s) =

E s X , defined for Is1 5 1, is called a probabilifygenerating function, or simply a generating function, of X . Find g x ( s ) for random variables with: (i) Geometric distribution. (ii) Binomial distribution. (iii) Poisson distribution.

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