If $X_1, X_2 $ are independent RVs. then are ${X_1}^2$ and ${X_2}^2$ are independent?

Asked Apr 27 '18 at 05:10

Active Apr 27 '18 at 05:23

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If $ X_1 , X_2 $ are independent RVs, then are ${X_1}^2 \,and\, {X_2}^2 $are independent?

P.S: this came up when i was working on the condition for which $Var({X_1 X_2})=Var({X_1}) Var({X_2})$

My Intuition says yes , but Covariance formula doesnt seem to work.

edited Apr 27 '18 at 05:23

spaceisdarkgreen

asked Apr 27 '18 at 05:10

DRPR

1

If $X$ and $Y$ are independent then $f(X)$ and $g(Y)$ are also independent where $f$ and $g$ are measurable functions. So your intuition is correct. – StubbornAtom Apr 27 '18 at 05:24
See here: https://math.stackexchange.com/questions/8742/are-functions-of-independent-variables-also-independent – Math1000 Apr 27 '18 at 05:33

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