Question: 7.19 A random variable X has the Poisson distribution p(x; ) = e x /x! for x = 0, 1, 2, . . .

7.19 A random variable X has the Poisson distribution p(x; μ) = e

−μ μx /x! for x = 0, 1, 2, . . . . Show that the moment-generating function of X is MX (t) = eμ(e t −1) .
Using MX (t), find the mean and variance of the Poisson distribution.

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