[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 byfxy(x.y) = 2x2 + y? where Osxys1.(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) =O(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) =D VY) =D and Cov(X, Y) =D(Simplify your answers. Do not convert fractions into decimals.)(d) The variance of Z can be found as V(Z) =-(Simplify your answer. 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 xyx.y) = 2x2 + y² where 0sxys1, (b) Assume Z=X +Y and W= XY and traffic experts are interested in the expected values of Z and W. E(Z) =D and E(W) =D (Simplify your answers. Do not convert fractions into decimals.) (C) Find the variances of X andY as well as the covariance between them. VX) =D. vY) =D and CovX, Y) =D (Simplify your answers. Do not convert fractions into decimals.) (d) The variance of Z can be found as V(Z) =. (Simplify your answer. 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 xyx.y) = 2x2 + y² where 0sxys1, (b) Assume Z=X +Y and W= XY and traffic experts are interested in the expected values of Z and W. E(Z) =D and E(W) =D (Simplify your answers. Do not convert fractions into decimals.) (C) Find the variances of X andY as well as the covariance between them. VX) =D. vY) =D and CovX, Y) =D (Simplify your answers. Do not convert fractions into decimals.) (d) The variance of Z can be found as V(Z) =. (Simplify your answer. 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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