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. 

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.

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

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.

5 . If , the solution set is exactly a subspace. (A) True. (B) False