# What is the expectation of $X^2$ where $X$ is distributed normally?

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.

Thanks

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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

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.