Multiple-choice problems. Please read the statements carefully, as no partial credit will be given. (Multiple choices are allowed for the last two questions.) (a) Which of the following statements is WRONG? A. If Xn a.s ?? X, then Xn p ?? X. B. If Xn L2 ?? X, then Xn p ?? X. C. If Xn D ?? X, then Xn p ?? X. D. If Xn D ?? M where M is a constant, then Xn p ?? M. E. If Xn D ?? X and Yn p ?? Y , then Xn + Yn p ?? X + Y . (b) Let X1, , Xn be an random sample of size n (iid) from a density f(x; ?) with an unknown parameter ?, ? ? ? ? R. Assume all regularity conditions hold. Which of the following statements is CORRECT? A. If E(X1) = ? and V ar(X1)

2. (2 points) Multiple-choice problems. Please read the statements carefully, as no partial credit will be given. (Multiple choices are allowed for the last two questions.) (a) Which of the following statements is WRONG? A. B. C. D. E. If X, 2 X, then X,, i) X. If X, E} X, then X,, i) X. If X, i} X, then X,, i) X. If X, i} M where M is a constant, then X,, i) M. Ian irX and Y, i) Y, thenX,,+Y,, in+Y. (b) Let X1, - - - ,X,, be an random sample of size an. (iid) from a density f(:r; 3) with an unknown parameter 6, 6 E O C IR. Assume all regularity conditions hold. Which of the following statements is CORRECT? A. If E(X1) = 6 and Vor(X1) XY. IfX, ix and Y, 3) Y, then an, 3)XY. IfX, x and Y, 3) Y, then an, 3)XY. IfX, anndniX,thean>Yn. . 1an 3) X and K, 3} M, where Mis aconstant, then X,,+Y,, 3} X+M