Given two continuous random variables X and Y with joint pdf

$f(x,y)=1$ if $0 leq X leq 1$ and $0 leq y<1 $

I want to find $E(|X-Y|)$

What I have done so far is to calculate marginal $F_x$ and $F_y$ which both are 1 in my case and then using the marginal to calculate $E(X)$ and $E(Y)$ but I think that I am making some mistake as I think that the expected value should be positive for all cases where $X<Y$.

What would be the general recommended method to solve problems like this?

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#### Best Answer

You need to divide your area $[0, 1]$ to two: where $X > Y$ and where $Y geq X$. Next you can simplify $|X – Y|$ in each area and take integral over each area.

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