Suppose X and Y are independent and follow uniform distribution (-a,a). How do we find the distribution of X-Y? I tried finding the area with the help of a diagram for cases when x-y>0 and x-y<0. I want to know what is the right way to do it.

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    $\begingroup$ Please add the self-study tag & read its wiki. Then tell us what you understand thus far, what you've tried & where you're stuck. We'll provide hints to help you get unstuck. Please make these changes as just posting your homework & hoping someone will do it for you is grounds for closing. $\endgroup$ May 12, 2021 at 8:20
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    $\begingroup$ Consider that $-Y$ and $Y$ has the same distributios, and have a look at stats.stackexchange.com/questions/41467/… $\endgroup$ May 12, 2021 at 8:23
  • $\begingroup$ Who knows what the "right" way might be -- but many different ways are given (in great detail) at stats.stackexchange.com/questions/41467. $\endgroup$
    – whuber
    May 12, 2021 at 15:54

1 Answer 1


So the individual means of X and Y are both 0, and so the mean of (X - Y) will also be 0.

The covariance of the two is 0, so we can just add up the variances. The variance of one variable is $(2a)^2 / 12=a^2/3$, so the variance of (X - Y) will be $2a^2 / 3$.


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