 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2010/ia/paper-2/4f/b/ii/solution

Perfect correlation means an affine relation almost surely: there are constants

a \neq = 0, b

such that

Y = a X + b

a

is the sign of the correlation coefficient. More precisely, equality in the Cauchy-Schwarz inequality gives

\frac{Y - E Y}{Var Y} = ρ (X, Y) \frac{X - EX}{Var X} almost surely .

 New to topics? Read the docs here!