3. Suppose that the conditional expectation of Y, given X = x, is linear in x, i.e.,

E(Y | X = x) = a + bx for some constants a and b. The aim of this exercise is to deter-

mine the values of a and b.

(a) Compute ?Y = E(Y) using the law of total expectation and

deduce that a and b satisfy a + b?X = ?Y.

(b) Compute E(XY) using the law of total expectation and deduce that a and b satisfy a?X + bE(X2) = E(XY).