Question: 20. Let X be a random variable whose moment generating function M(t ) exists for |t | < h, where h > 0. Let N

20. Let X be a random variable whose moment generating function M(t ) exists for |t | < h, where h > 0. Let N be a random variable taking positive integer values such that P(N = k) > 0 for k = 1, 2, . . . .

Show that M(t ) =

∞X k=1 P(N = k)E(et X | N = k) for |t | < h.

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