1. The problem statement, all variables and given/known data Prove the following: Let [tex]\rho[/tex] be the correlation coefficient. Prove: [tex] \rho(X, Y) = 1 \iff P(Y=aX+b) = 1[/tex] 2. Relevant equations [tex] \rho(X, Y) = cov(X,Y)/\sigma_x\sigma_y [/tex] 3. The attempt at a solution I have no idea how to prove this, I know that rho must lie between 1 and -1 (inclusive) and that values close to 1 indicate that high values of X must go with high values of Y. But I don't know how to formally prove the above problem.