Question 1 (10 points) P d Assuming X, a > 0, Yb 0 and Z Z~N(0,1), and using the properties below, Xn n find the limiting distributions of the ten sequences of random variables below. Continuous Mapping Theorem P If Xna and Yn > b and g(x, y) is continuous at (a, b) then g(xn, Yn) g(a,b) Slutsky's Theorem If Xn d P X and Y b and g(x,b) is continuous for all x in the support of X then d g(xn, Yn) g(x,b) (1) X (2) xn (3) Xn Yn (4) Xn+Yn (5) Xn/Yn (6) 2Zn (7) Zn + Yn (8) XnZn (9) Z (10) 1/Zn