Q:

Finding Standard Deviation from MGF

I a working on a problem and am a little bit confused at how to approach solving it.
The problem: Given the MGF F(t) = $1\over(1-2500t)^4$ 
Calculate the SD.
Do we need to do some substitution with like $\mathscr N$ ~ (0,1) with sigma and mu? Or find the Var and square root it?
More broadly, how do we find the Standard Deviation of a Moment Generating Function?

A:

You don't find SD of a MGF ... you find SD of a random variable, cmon. 
Let $X$ be your random variable, then MGF of $X$ is basically $M_X(t) = E[e^{Xt}]$
If you check your textbook, you will find a nice property for the MGF, namely the n-th derivative of M evaluated at zero is equal to $E[X^n]$
Now, SD = $\sqrt{Var(X)} = \sqrt{E[X^2] - E[X]^2}$.
Can you take it from there?

