Question: A random variable X has the discrete uniform distribution f(x; k) = 1 k , x = 1, 2,..., k, 0, elsewhere. Show that the

A random variable X has the discrete uniform distribution f(x; k) = 1 k , x = 1, 2,..., k, 0, elsewhere.

Show that the moment-generating function of X is MX(t) = et

(1 − ekt)

k(1 − et) .

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