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

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

e μ /x! for x = 0, 1, 2, …. Show that the moment-generating function of X is x – 1 X

–μ x Using M (t), find the mean and variance of the Poisson distribution.

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