In my problem, I have the moment-generating function on a random variable X. The function is:

$\displaystyle M_{X}(t)=\frac{1}{(1-2500t)^4}$

I am to determine the standard deviation.

I have no idea how to begin. I know that the standard form for a moment-generating function is:

$\displaystyle M_{X}(t)=E[e^{tx}]$

Neither my book nor Wikipedia give any clues as to what the variables mean. I certainly hope this is a situation where t (used in one explanation) = t (used in others). All I really know is, X is a random variable.

Should I just be trying to transform what I am given into the E[e^{tx} form?

Am I trying to determine what t is?

Is the form of the function I was given an indication of a specific type of continuous distribution? None of the distributions I've seen (uniform, normal, etc.) has a moment-generating function that looks like that.