Here is a question on correlation coefficients:

M := [abbc]

The eigenvalues of M equal

1 = (a+c+d)/2

2 = (a+c-d)/2

where d := the square root of (a² +4b²+c²-2ac)

The eigenvectors equal

u1 = [(ac+d)/2b1]

u2 = [(acd)/2b1]

Use this to prove that for any zero-mean random variables X and Y if X,Y=1 then

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