Question

Let M_{x}(t) be a moment generating function. Let
S_{x} (t) = [M_{x} (t)]^{2}− M_{x}
(t). Prove that S ′_{x}(0) = µ_{X}.

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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