Problem 21. (3.0 %) Let X_i,i = 1,2, ... be independent random variables all distributed according to the pdf f_X(x) = 1 for 0 ≤ x ≤ 1. Definc Y_n = X₁X₂X₃... X_n for some integer n. Then var(Y_n) is equal to
(A)
(B)
(C)
(D)

Problem 17. (2.5 %) N people put their hats in a closet at the start of a party, where each hat is uniquely identifed. At the end of the party each person ran- domly selects a hat from the closet. Suppose N is a Poisson random variable with parameter. If X is the number of people who pick their own hats, then E[X] is equal to (A) (B) (C) (D)1

Problem 18. (3.0 %) Suppose X and Y are Poisson random variables with parameters respectively, where X and Y are independent. Define W = X + Y, then, (A) W is Poisson with parameter (B) W is Poisson with parameter (C) W may not be Poisson but has mean equal to(D) W may not be Poisson but has mean equal to

Problem 19. (3.0 %o) Let X be a random variable whose transform is given by MX(s) = (0.4 +0.6es)50. Then, (A) P(X =0) = P(X = 50) (B) P(X = 51) ＞0 (C) P(X = 0)=0.450 (D) P(X= 50) = 0.6

Problem 20. (3.0 %) Let Xi,i = 1,2, ... be independent random variables all distributed according to the pdf fX(x) = x/8 for 0 ≤ x ≤ 4. Let S = . Then P(S ＞3) is approximately equal to (A) (B)(C) (D)

Problem 22. (3.0 %) Suppose you play a matching coin game with your friend as follows. Both you and your friend have a coin. Each time, you two reveal a side (i.e. H or T) of your coin to each other simultaneously. If the sides match, you WIN a 1 from your friend if sides do not match then you lose a 1 your friend. You decide to go with the following strategy. Every time, you will toss your unbiased coin independently of everything else, and you will reveal its outcome to your friend (your friend does not know the outcome of your random toss until you reveal it). Then, (A) On average, you will lose money to your smart friend (B) On average, you will lose neither lose nor win. That is, your average gain/loss is 0. (C) On average, you will make money from your friend

1.國防政策可以反映國家國防體制運作的目的與取向，另一方面還可以透過國防政策的單一化，爭取國人認同，擴大國防政策的效益。(A)O(B)X

2.我國國防政策並非局限於軍備、兵力等軍事事務，而是任何與維護國防安全的事務，如：人、物力動員等，都屬於其範疇。(A)O(B)X

3.國防政策透明化不局限軍軍事務，涵蓋範疇廣，主要目的在期望擴大國防政策的效益。(A)O(B)X

4.我國依「國防法」有關國防政策的指導，評估國內外戰略環境與趨勢。(A)O(B)X

5.確保國家安全是國防的主要目的。(A)O(B)X