Let $X \sim \mathcal{N}(0,9)$ have mean $0$ and variance $9$. Find the expected value of $X^2(X+1)$.
2026-04-01 06:10:04.1775023804
Let $X \sim \mathcal{N}(0,9)$ have mean $0$ and variance $9$. Find the expected value of $X^2(X+1)$
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We seek the mean of $X^3+X^2$. The first term makes no contribution, because the distribution is symmetric. The second term has mean $9+0^2=9$, so the answer is $9$.