The joint pdf of X and Y is fyx = 1 for 0<x<1, x<y<x+1
Compute the covariance and the correlation of X and Y.
I figured out the covariance and checked that it is indeed 1/12.
So, my E[X] = 1/2 and E[Y] = 1 are correct too.
For E[Y] = integral(0 to 2)integral(y-1 to y) of y dxdy = 1 (this is correct, just to help with bounds)
I can't figure out the ****correlation**** though.
Corr(X,Y) = Cov(X,Y)/[sqrt(Var[X]Var[Y])]
For the variances I had
Var[X] = 1/3 - 1/2^2 = 1/12
Var[Y] = 8/3 - 1^2 = 5/3
My answer came to Corr(X,Y) = 0.2227 but that's wrong !!! and i can't find the mistake...
Answer is 0.7071
I think my bounds are wrong (they often are!) but that's what my sketch looks like :/
x goes from 0 to 1 and is bounded by the lines y=x and y=2x...
E[y^2] = I(0 to 2)I(y-1 to y) y^2 dxdy = I(0 to 2) y^2 dy = 8/3 ...