Let X be a Poisson random variable with parameter k. (a) Show that the moment generating function for X is given by ?? (?) = ?^(?(?^?−1)) (b) Show that E(X) = k. (c) Show that Var (X) = k.

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Let X be a Poisson random variable with parameter k.

(a) Show that the moment generating function for X is given by

?? (?) = ?^(?(?^?−1))

(b) Show that E(X) = k.

(c) Show that Var (X) = k.

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