(i) In reference to Exercise 12 and 13, and by writing (XY) = [(XY)|X], show that (XY)...

Question:

(i) In reference to Exercise 12 and 13, and by writing ε(XY) = ε[ε(XY)|X], show that ε(XY) = (1(2 + ((1(2.
(ii) Use the definition of the conversance of two r.v.s X and Y (with finite second moments), Cov (X, Y) = ε[(X - εX)(Y - εY)] = ε(XY) - (εX) (εY), in order to conclude that, in the present case, Cov(X, Y) = ((1(2.
(iii) From part (ii), conclude that, in the present case, the correlation coefficient of the r.v.s X and Y, ((X, Y), is equal to (?