exam22018.pdf

# Compute the expected value of the total damage x y e

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(d) (7 points.) Compute the expected value of the total damage X + Y . (e) (3 points.) Are X and Y independent? Justify your answer; no credit for guessing the right answer with no work. (f) (3 points.) Are X and Y uncorrelated? Justify your answer; no credit for guessing the right answer with no work.

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ECSE-2500 Engineering Probability Fall 2018 Exam 2 Page 10 7. (15 points.) Two random variables X and Y have means and variances given by E ( X ) = 3, E ( Y ) = 4, σ 2 X = 4, and σ 2 Y = 9. The correlation coefficient between the two random variables is ρ = 1 3 . (a) (3 points.) Compute E ( Y - X ). (b) (7 points.) Compute Var( Y - X ). (c) (5 points.) Using the Chebyshev inequality, find a lower bound for P ( X - 4 < Y < X + 6). Note that this is the same as P ( | Y - X - 1 | < 5).
ECSE-2500 Engineering Probability Fall 2018 Exam 2 Page 11 Blank page for extra work
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