I have a problem where I am faced with the term $\operatorname{Cov}[XY,XZ]$. However, I do not know what to do with this term. I may assume that $Y$ and $Z$ are independent and that $X$ is independent with both $Y$ and $Z$. I know $E[XY]$, $V[XY]$, $E[XZ]$ and $V[XZ]$. So my question comes down to this. What is the covariance of independent random variables when they both are multiplied with the same random variable can we just see it as if the $X$ was a constant i.e. the covariance is still zero?
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Dups: https://stats.stackexchange.com/questions/389662/covariance-of-products-of-dependent-random-variables and https://stats.stackexchange.com/questions/203457/law-of-total-covariance-for-products-of-random-variables – kjetil b halvorsen Mar 13 '19 at 11:36