X and Y are independent continuous random variables with probability density functions (PDFs) shown below. What is the probability of P(-1

(A) 1/4
(B) 2/3
(C) 3/4
(D) 5/8
(E) none of the above.

39.利用主線圈及次線圈之圈數不同來改變交流電電壓之變壓器，是利用？ (A)集膚效應 (B) 皮爾定律 (C)繞線原理 (D) 法拉第定律

40.調整以下那個儀器操作鈕，可改變離距與導電率曲線之夾角值？ (A)相位鈕 (B)離距鈕 (C)導電率鈕 (D)頻率鈕

複選題十五. Consider the famous hat problemn. Suppose that n pcople throw their hats in a box and n each picks one hat at random. (Each hat can be picked by only one person, and cach assi of hats to persons is equally likely) Let X be a random variable that ropresents the number of people that get back their own hat. Which of the following statemnents is/are true? (A) When n =3, P(X =3)= (B) When n = 3, P(X = 1)= (C) When n = 4, P(X = 3) = 0. (D) When n = 4, E[X] = 2. (E) When n = 5, E[X] = 1.

複選題十六. Consider the famous hat problem as in the previous problem. Let X, be a random variable that takes value 1 if the ith person selects his/her own hat, and takes value O otherwise. Let cov(Y, Z) = [Y . Z] -E[Y] ㆍE[Z] be the covariance of two random variables Y and 2. Which of the following statements is/are true? (A) When n = 4, cov(X4, X4) is .(B)When n = 4,cov(X1,X2)=(C) When n = 4, va=2. (D) When n = 4, Xi and Xz are statistically independent. (E) For any two random variables Y and Z, cov(Y, Z) ≥0.

15. (5%) The random variables X1, X2,X3 have the joint Gaussian pdf: What is the marginal Goint) pdf of Xi and X3? (A) 0. (B) (C) (D)(E) None of the above. 

16. (5%) According to Problem 15 above, for the 3✖3 covariance matrix of (X1.X2,X3), determine the correct element values Ki of the covariance matrix. (A) (B) (C)(D) (E) None ofthe above.

1. If , the solution set may be a subspace. (A) True. (B) False.

2. If , the solution set is not a subspace. (A) True. (B) False.

3. If , the solution set may be or may not be a subspace. (A) True. (B) False.

4. If , the solution set is not a subspace. (A) True. (B) False.