Problem 14. (2.5 %) Let X and Y be two continuous random variables. Then, (i) E[XY] = E[X]E[Y] (ii) E(X2 + Y2] = E[X2] + E[Y2] (iii)fx+x(x+y)=f.x(x).fr(y) (iv) var(X+Y)=war(X)+var(Y)

Problem 7. (2.5 %) Consider two random variables X and Y, each taking val- ues in {1,2,3}. Let their joint PMF be such that for any 1 ≤ x, y ≤ 3,Then, (i) X and Y can be independent or dependent depending upon the strictly positive values(ii) X and Y are always independent(iii) X and Y can never be independent