Suppose $f_{X,Y} (x, y) = 3/14*(xy + x) , \space 0 ≤ x ≤ 2, \space0 ≤ y ≤ x$

Find $E[XY]$.

How do you find the expected value of two random variables like this? I know the properties of E[X] but I never studied E[XY].

Do I just assume they are independant? It doesn't look like it, because $f_X(x) * f_Y(y)$ does not equal $f_{X,Y}$...

  • 2
    $\begingroup$ Just find the RHS of $\mathbb EXY=\int\int xyf_{X,Y}(x,y)dxdy$. $\endgroup$ – drhab Jun 22 '17 at 11:33
  • 1
    $\begingroup$ @drhab oh. That makes sense $\endgroup$ – user3026388 Jun 22 '17 at 11:34

As drhab mentioned, the answer is simply:



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