# Chi-squared expected value

• Oct 8th 2009, 04:42 PM
akolman
Chi-squared expected value
Hello, I need to get the expected value of a chi-squared distribution with one degree of freedom, using the following formula with the pdf:

$E[Y]=\int_0^\infty y f(y) dy$

So, $E[Y]= \int_0^\infty y \frac{1}{\sqrt{2 \pi y}} e^{-y/2}dy = \int_0^\infty \frac{\sqrt{y}}{\sqrt{2 \pi}} e^{-y/2}dy$

I have no idea how to deal with that integral. I know that there are easier ways to do it, but I am supposed to solve it using this integral. Thanks in advance.
• Oct 8th 2009, 05:25 PM
mr fantastic
Quote:

Originally Posted by akolman
Hello, I need to get the expected value of a chi-squared distribution with one degree of freedom, using the following formula with the pdf:

$E[Y]=\int_0^\infty y f(y) dy$

So, $E[Y]= \int_0^\infty y \frac{1}{\sqrt{2 \pi y}} e^{-y/2}dy = \int_0^\infty \frac{\sqrt{y}}{\sqrt{2 \pi}} e^{-y/2}dy$

I have no idea how to deal with that integral. I know that there are easier ways to do it, but I am supposed to solve it using this integral. Thanks in advance.

Read this: Gamma function - Wikipedia, the free encyclopedia