(i) In reference to Exercise 12 and 13, and by writing (XY) (XY) X , show that (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) (X X)(Y Y) (XY) (X) (Y), 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 (

Question: (i) In reference to Exercise 12 and 13, and by writing (XY) = [(XY)|X], show that (XY) = (1(2 + ((1(2. (ii) Use the definition

(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 (?

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