Let $X$ be a standard Normal random variable. Let $Y$ be a random variable with $P(Y=-1)=P(Y=1)=1/2$ . Then I can show that $YX$ also follows Standard Normal distribution.
My question is: How to show that $YX$ and $X$ are NOT independent ?
2026-03-28 16:04:06.1774713846
On the indendence of two standard Normal random variable
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Let $A=(|X|\le x)$ and $B=(|XY|\le x)$. If independent, $P(A\cap B)=P(A)P(B)$. However, $P(A\cap B)=P(A)$.