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
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.