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Let Mx(t) be a moment generating function. Let Sx (t) = [Mx (t)]2− Mx (t). Prove...

Let Mx(t) be a moment generating function. Let Sx (t) = [Mx (t)]2− Mx (t). Prove that S ′x(0) = µX.

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Answer #1

We are given that MX(t) is the moment generating function of a random variable X and a function of this MGF given by:

Now, we know that:

Substituting equations (2) and (3) in equation (1), we get:

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