What is $E[X]$ of $V^2$ given that $V\sim\mathcal N(0,\sigma^2)$?

Question

I am trying to compute the expected value of a function $V^2$, given that $V$ is a normal random variable with mean $\mu= 0$ and variance $\sigma^2$.

Answer 1

This is just $\mathbb E[V^2]$. Since $\operatorname{Var}(V)=\mathbb E[V^2] - \mathbb E[V]^2$ it follows that $$\mathbb E[V^2] = \sigma^2. $$