To get the expected value of E(X),E(Y) and E(X,Y) given:
fX,Y(x,y)=3x
where 0≤x≤y≤1.
My solution is, first get the margin distribution:
fx(x)=3x(1−x)fy(y)=32y2
Then calculate the expected value:
E(X)=∫y03x2(1−x)dx=y3−34y4E(Y)=∫1x32y3dy=38(1−x4)
and
E(XY)=∫y0∫1xxy⋅3xdydx=12y3−310y5
However, my calculated expected values contain variable x and y, do I make some mistakes?
Answer
[after you added the joint distribution of X,Y]:
to find EXY use
∫10∫y0xyf(x,y)dxdy
Can you handle the rest?
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