# Thread: Squared Standard Normal Random Variables

1. ## Squared Standard Normal Random Variables

My probability & statistics textbook states that the mean of a squared standard normal random variable is 1, but it doesn't explain how and I'm extremely confused. It seems to me that a squared standard normal random variable's mean should just be the standard normal random variable's mean squared, which would be 0^2 = 0. Can anybody help explain my error? Thanks!

2. Originally Posted by lonrisbuel
My probability & statistics textbook states that the mean of a squared standard normal random variable is 1, but it doesn't explain how and I'm extremely confused. It seems to me that a squared standard normal random variable's mean should just be the standard normal random variable's mean squared, which would be 0^2 = 0. Can anybody help explain my error? Thanks!
Your errors are several and include the error of thinking that $\displaystyle E(X^2) = [E(X)]^2$ (if this was true then the variance of all distributions would be zero).

Read Chi-square distribution - Wikipedia, the free encyclopedia