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- Let X and Y be independent, taking on {1,2,3,4,5} with equal probabilities. E((X+Y)2)=?If X and Y are independent, then the conditional expectation of Y. given X is equivalent to: E(Y|X) (There is only one correct answer this time.) E(XY) E(Y) E(X)A fair dice rolls. Let X be the number on the dice and Y be 0 for even X and 1 for odd. Find covariance of X and Y?
- Determine whether each is dependent or not, based on the rules for independence. 1. P(A)=1/5,P(B)=3/10,P(AandB)=3/100 ["", ""] 2. P(A)=13/20,P(B)=7/10,P(AandB)=91/200 ["", ""] 3. P(A)=3/5,P(B)=2/5,P(AandB)=6/25 ["", ""]assume that Pr[A] = 0.45, Pr[B] = 0.35, and Pr[A n B] = 0.25. Compute the following conditional probabilities: (1) Pr[A|B] = (2) Pr[B|A] =A class contains 30 students. The probability of failing in one of the courses for each student is 0.02, but there is no chance to fail in more than one course. You know that a student failed in a course, the probability that the fail reason in non-attendance is 0.03. All other fail reasons are low average. The examinations are private, so the results are mutually independent. Let X and Y be the numbers of failed students due to non-attendance and due to low average, respectively, in that class this semester. Find the joint MGF
- question 8 8. Which of the following sets of expectation islare possible? E(X) = 3, E(Y) = 2, E(x?) = 8, E(Y) = 8 and E (XY) = 0. E(X) = 3, E(Y) = 2, E(x2) = 10, E(Y) = 2 and E (XY) =-5. E(X) = 3, E(Y) = 2, E(x?) = 10, E(Y) = 8 and E (XY) = 8. E(X) = 3, E(Y) = 2, E(X) = 13, E(Y) = 20 and E (XY) = 0. Previous Save For Later Nexta. Find the probability that the device A functions but the device B does not. b. Find the probability that the device A or the device B or both function. c. Find the probability that the circuit operates. d. It is known that the circuit is operating, find the probability that device A is functional.Calculate the conditional expectation of Y when X = 2. E(YX2)
- (ii) At a Harford university, the probability that a student takes calculus and agriculture in the same semester is 0.09. The probability that a student takes agriculture is 0.15. The probability that a student takes calculus is 0.6. a. State, giving a reason in each case whether probability of calculus and probability of agriculture are independent b. Find the probability that a student is taking calculus, given that he or she is taking agriculture.The circuit shown below operates if and only if there is some path of functional devices from left to right. The probability that each device functions is shown for each device and the devices operate independently of each other. What is the probability that the circuit operates? 0.9 0.9 0.8 0.95 0.95 0.9 (A) None of these (B) 0.5263 (C) 0.1642 (D) 0.9850 (E) 0.9702