Originally Posted by

**kid funky fried** I am trying to find the expected value of X.

$\displaystyle

f(x) = 2x e^{ - x^2 } dx,

for all x \in R = (0,\infty )

$

$\displaystyle

u = E[X] = \int_R^{} {x*f(x)} dx = 2\int\limits_0^\infty {x^2 e^{ - x^2 } dx}

$

I could not find any integral table to make this any easier and my trusty ti-92+ would not integrate this either.

So, I have tried to solve by letting

$\displaystyle

u = x^2 and\_du = 2xdx

$

Again, I have gotten nowhere.

Any suggestions would be appreciated.

Thanks.

Note:

I just found a table that lists the integral = .5*(pi)^1/2.