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Suppose $X$ and $I$ and independent, $X$ has a standard normal distribution and $I$ take values $1$ and $-1$ with equal probabilities.

Let $Y = IX$. How would I find the distribution of $Y$ and $X+Y$? and $E(Y|X)$, $E(Y^2|X)$?

Thanks so much!

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    Multiplying I has 1/2 chance of mirroring X about 0. So, symmetric distributions about $x=0$ are still themselves. Y follows the same normal distribution.2012-08-21

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