Answer with full steps please

Q6 (15 marks) Let X and Y have the joint p.m.f. described in the table: ( x, y) (1,2) (1,3) (2, 2) (2,3) (3,2) (3, 3) f(x,y) 2/15 1/15 4/15 2/15 3/15 3/15 Calculate the correlation coefficient between X and Y. Q7 (15 marks) Suppose that X and Y are independent random variables both following Geometric distribution with parameter p. Find the conditional pmf of X given X + Y = n. (Hint: P(X = x |X + Y = n) = P ( X = x , X + Y = n ) _P(X =x,Y=n-x) P(X +Y=n) P ( X +Y=n) ...)