Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I know that if $X$ were distributed as a standard normal, then $X^2$ would be distributed as chi-squared, and hence have expectation $1$, but I'm not sure about for a general normal.


share|cite|improve this question
if $ Y \sim \mathcal{N}(\mu,\sigma^2)$ then you have $ Y = \sigma X +\mu $ where $ X \sim \mathcal{N}(0,1)$ – math Jan 14 '12 at 16:03
up vote 17 down vote accepted

Use the identity $$ E(X^2)=\text{Var}(X)+[E(X)]^2 $$ and you're done.

Since you know that $X\sim N(\mu,\sigma)$, you know the mean and variance of $X$ already, so you know all terms on RHS.

share|cite|improve this answer
Haha, thanks. I didn't think of that. – maliky0_o Jan 14 '12 at 16:04

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.