Chapt 6e

# Chapt 6e - 6.13 Problems 237 Section 6.8 Two Functions of...

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6.13 Problems 237 Section 6.8: Two Functions of Two Random Variables 6.21 Two independent random variables X and Y have variances σ 2 X = 9 and σ 2 Y = 25, respectively. If we define two new random variables U and V as follows, U = 2 X + 3 Y V = 4 X - 2 Y a. find the variances of U and V . b. find the correlation coefficient of U and V . c. find the joint PDF of U and V in terms of f XY ( x , y ) . 6.22 Two random variables X and Y have zero mean and variances σ 2 X = 16 and σ 2 Y = 36. If their correlation coefficient is 0.5, determine the following: a. The variance of the sum of X and Y . b. The variance of the difference of X and Y . 6.23 The joint PDF of two continuous random variables X and Y is given by f XY ( x , y ) = braceleftbigg e - ( x + y ) 0 < x < , 0 < y < 0 otherwise If we define the random variable W = X / Y , find the PDF of W . 6.24 Let X and Y be two independent random variables that are uniformly dis- tributed between 0 and 1. If we define Z = XY , find the PDF of Z .

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