[Joint PDFS will be covered in Week 7] Let the random variables X and Y be the portions of the time in a day that two alternative routes between Topkapi and Uskudar have congestion (X for Route 1 and Y for Route 2). The joint PDF is given by fy y(x.y) = 2x +y where 0sx.ys1. (a) Assume g(x) and h(y) are the marginal PDFS of X and Y, respectively. Since fy y (x.y) is not equal to g(x)h(y). it can be concluded that X and Y are not independent. (b) Assume Z =X+Y and W=XY and traffic experts are interested in the expected values of Z and W. E(Z) = and E(W) = (Simplify your answers. Do not convert fractions into decimals.) (c) Find the variances of X and Y as well as the covariance between them. v(X) = V(Y) =D and Cov(X,Y) =D (Simplify your answers. Do not convert fractions into decimals.)
[Joint PDFS will be covered in Week 7] Let the random variables X and Y be the portions of the time in a day that two alternative routes between Topkapi and Uskudar have congestion (X for Route 1 and Y for Route 2). The joint PDF is given by fy y(x.y) = 2x +y where 0sx.ys1. (a) Assume g(x) and h(y) are the marginal PDFS of X and Y, respectively. Since fy y (x.y) is not equal to g(x)h(y). it can be concluded that X and Y are not independent. (b) Assume Z =X+Y and W=XY and traffic experts are interested in the expected values of Z and W. E(Z) = and E(W) = (Simplify your answers. Do not convert fractions into decimals.) (c) Find the variances of X and Y as well as the covariance between them. v(X) = V(Y) =D and Cov(X,Y) =D (Simplify your answers. Do not convert fractions into decimals.)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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