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Two variables $X_1, X_2$ are independent and identically distributed as $N(0,1)$. I need to find

Cov($X_1$, $X_1 X_2$).

Thanks!

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\begin{align} {\rm cov}(X_1, X_1 X_2) &= E(X_1^2 X_2) - E(X_1) E(X_1 X_2) \\ &= E(X_1^2) E(X_2) - E(X_1)^2 E(X_2) \\ &= 1 \times 0 - 0^2 \times 0 \\ &= 0 \end{align}

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