1. ## 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:

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

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

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.

2. 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:

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

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

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