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