The c.d.f. of a random variable X is given by the following formula
F(x) = 1 - e-x2 x≥0
Find M(t). Moment generating function.
The Attempt at a Solution
I've found the pdf as
f(x) = F'(x) = 2xe-x2 x≥0
To determine M(t) I need to do the following
M(t) = E(etX) = ∫etx 2xe-x2
Then I'm not sure how to go about integrating. Any ideas or clues to point me in the right direction will be greatly appreciated. Thanks.