X and Y are continuous R.V. with values X in (0,1), Y in (0,1) and joint PDF f(x,y)=6(x-y)^2, compute the covariance, Cov(X,Y).
Thank you
here E(X)=
x*f(x,y) dx dy =
x*(x2+y2-2xy) dx dy =
(x3+xy2-2x2y)
dx dy
=
(x4/4+x2y2/2-2x3y/3)
|10 dy =
(1/4+y2/2-2y/3)
dy =(y/4+y3/6-y2/3)|10
=(1/4+1/6-1/3)=1/12
similarly E(Y)=
y*f(x,y) dx dy=1/12
E(XY)=
xy*f(x,y) dx dy=1/36
hence Cov(X,Y)=E(XY)-E(X)*E(Y)=1/36-(1/12)*(1/12)=3/144=1/48
X and Y are continuous R.V. with values X in (0,1), Y in (0,1) and joint...
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