Saturday, 27 August 2016

probability - Calculate the expected value



To get the expected value of E(X),E(Y) and E(X,Y) given:

fX,Y(x,y)=3x
where 0xy1.



My solution is, first get the margin distribution:
fx(x)=3x(1x)fy(y)=32y2




Then calculate the expected value:
E(X)=y03x2(1x)dx=y334y4E(Y)=1x32y3dy=38(1x4)



and
E(XY)=y01xxy3xdydx=12y3310y5



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
10y0xyf(x,y)dxdy
Can you handle the rest?



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