Exercise 4.1 Uncorrelated does not imply independent.

Let X U(1, 1) and Y = X^2. Clearly Y is dependent on X (in fact, Y is uniquely determined by X). However, show that (X, Y )=0. Hint: if X U(a, b) then E[X]=(a + b)/2 andvar [X]=(b a)2/12.