Problem # 3 Another variation on a somewhat familar theme...: Let random variables X and Y reflect the winning rates of two gamblers, i.e., each takes value in [0,1] and measures the performance in terms of the number of winning bets divided by the total number of bets. It has been established that their joint PDF is: Sx,y(x,y) = { 0 12x3y² 0≤ x ≤ 1, 0 ≤ y ≤ 1, otherwise a) Find the expected winning rates E[X], E[Y], the covariance Cov(X, Y] and the expected winning ratio E[X/Y]. b) Find their (n, k) joint moment about the origin. c) Are X and Y uncorrelated, orthogonal and/or independent?

Problem # 3 Another variation on a somewhat familar theme...: Let random variables X and Y reflect the winning rates of two gamblers, i.e., each takes value in [0,1] and measures the performance in terms of the number of winning bets divided by the total number of bets. It has been established that their joint PDF is: Sx,y(x,y) = { 0 12x3y² 0≤ x ≤ 1, 0 ≤ y ≤ 1, otherwise a) Find the expected winning rates E[X], E[Y], the covariance Cov(X, Y] and the expected winning ratio E[X/Y]. b) Find their (n, k) joint moment about the origin. c) Are X and Y uncorrelated, orthogonal and/or independent?

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter1: Functions

Section1.2: The Least Square Line

Problem 4E

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