If $X$ and $Y$ are independent random variables, does it follow that $X^2$ and $Y$ are independent?

Question

If $X$ and $Y$ are independent random variables, then can I say that $X^2$ and $Y$ are independent?

Any function of $X$ is independent of any function of $Y$. – Stefan Hansen Dec 05 '14 at 11:46 — Stefan Hansen, Dec 05 '14 at 11:46

score 0 · Answer 1 · answered Dec 05 '14 at 11:49

0

Yes, if X and Y are independant, for all functions $\phi_1$ and $\phi_2$, $\phi_1(X)$ and $\phi_2(Y)$ are independant.

answered Dec 05 '14 at 11:49

Droplet

thank you for the comment. you know where i can find proof to this? – Amit Dec 05 '14 at 11:51
http://math.stackexchange.com/questions/8742/are-functions-of-independent-variables-also-independent You can find different ideas of proofs in the answers of this question. – Droplet Dec 05 '14 at 12:03

1 Answers1