49. Let X have variance 2 x and let Y have variance 2 y . Starting with...

49. Let X have variance σ2 x and let Y have variance σ2 y . Starting with

Using the result that Var(Z) = 0 implies that Z is constant, argue that if Corr(X , Y ) = 1 or −1 then X and Y are related by Y = a + bx where the sign of b is positive when the correlation is 1 and negative when it is −1.

Transcribed Image Text:

show that 0 Var(X/ox + Ylo,) Now using that conclude that -1 Corr(X, Y) 0 Var(Xlox - Ylo,) -1 Corr(X, Y) 1