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[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.)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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[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 fx 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) = 15 ,V(Y) =| and Cov(X,Y) = (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.)
Transcribed Image Text:[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 fx 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) = 15 ,V(Y) =| and Cov(X,Y) = (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.)
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