# Expected value of squared normal

• January 25th 2010, 11:55 AM
mrfloyd
Expected value of squared normal
I need to find the expected value a N~(0,1) squared distribution. I realize this is a Chi Square distribution with k = 1. The expected value is therefore k = 1. However, I am having trouble taking the following integral to find the expected value:

Integrate y*exp(-y^4) from -inf to inf.

I'm sure there is a trick somewhere to figure it out but i can't find it!

Thanks
• January 25th 2010, 12:11 PM
CaptainBlack
Quote:

Originally Posted by mrfloyd
I need to find the expected value a N~(0,1) squared distribution. I realize this is a Chi Square distribution with k = 1. The expected value is therefore k = 1. However, I am having trouble taking the following integral to find the expected value:

Integrate y*exp(-y^4) from -inf to inf.

I'm sure there is a trick somewhere to figure it out but i can't find it!

Thanks

The expected value of $x^2$ is:

$E(x^2)=\int_{-\infty}^{\infty} x^2 p(x) \; dx$

which in this case comes to the variance of $x$

CB
• January 25th 2010, 03:03 PM
matheagle
The integral of an odd function from minus infinity to infinity is zero.
But I'm not sure if that is what you're asking.