(5%) Let X and Y have the joint probability density function f(x,y)=2, 0≤x≤y≤1. Which of the following is correct? (A) E[X] = 1 (B) E[Y] = 1/2 (C) E[Y2] =1/2 (D)Pr(o sX sY,O≤Y≤=1/2 (E) None of these

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.

(5%) Let X and Y have the joint probability density function f(x,y)=2, 0≤x≤y≤1. Which of the following is correct?
(A) E[X] = 1
(B) E[Y] = 1/2
(C) E[Y²] =1/2
(D)Pr(o sX sY,O≤Y≤=1/2
(E) None of these

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