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## Homework Statement

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(e

^{tX}) = ∫e

^{tx}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.