from zero to infinity,(adsbygoogle = window.adsbygoogle || []).push({});

and the first raw moment about zero is the first derivative of the mgf evaluated at t=0... then why do we need to integrate the function ?

Wouldn't the first raw moment just be e^tx.fx(x) dx, i.e the derivative of the function we just integrated ?

Why do we integrate and then find the derivative of the same function ?

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# If the moment generation function is the integral of e^tx.fx(x).dx

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