Is the square of the product of two independent random variables equal to the product of their squares?
For example: if W = XY, is W^2 = (XY)^2 = (X^2)(Y^2)?
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Random variables are just another word for functions, so given that their image lies in something that is commutative (e.g. $\mathbb Z, \mathbb R, \ldots$), that is the case. – Zag Dec 23 '22 at 14:50
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1Context? Assuming that $X,Y$ are real valued random variables then $XY=YX$ so there is no issue. But of course, not all random variables are real valued. If, say, $X,Y$ were matrix valued random variables, then we might not have $XY=YX$. – lulu Dec 23 '22 at 14:50
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Yes, both X and Y are real-valued. – MRG Dec 23 '22 at 15:03