Suppose that X and Y have a joint distribution with correlation 1 2 and that Var(X) Var(Y) 1 Show that b 1 2 is the unique value of b such that the correlation of X and X bY is also

Question: Suppose that X and Y have a joint distribution with correlation > 1/2 and that Var(X) = Var(Y) = 1. Show that b= 1/2

Suppose that X and Y have a joint distribution with correlation ρ > 1/2 and that Var(X) = Var(Y) = 1. Show that b=− 1/2ρ is the unique value of b such that the correlation of X and X + bY is also ρ.

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