We have an urn with 6 red balls and 4 green balls. We draw balls from the urn one by one without replacement, noting the order of the colors, until the urn is empty. Let X be the number of red balls in the first five draws, and Y the number of red balls in the last five draws. Compute the covariance Cov(X,Y).
where Ii=1 if red and Jj=1 if green.
Cov(X,Y)= E(XY)-E(X)E(Y) E(XY)=E(I1J6)+E(I1J7)+...+E(I5J10)=25*E(I1J6)
I don't know I am doing it right. Are there other ways to solve this?