I need help. The problem is this:

X is an exponentially distributed random variable with p.d.f.

f(x) =

0<x<infinity

Show that the m.g.f. of X is for , and use this to find E(X) and Var(X).

I have no idea what to do with this problem or where to start. Please help point me somewhere? The only thing I could think of to potentially do is to undo the p.d.f. to get the original random variable, but...yeah. I'm really, really lost.