Exercises1. Suppose that X1 and X2 are random variables with zero mean and unitvariance. If the correlation coefficient of X1 and X2 is –0.5, then what is thevariance of Y = =k2Xk ?Lk=12. If the joint density of the random variables X and Y isif (x, y) E { (x,0), (0, -y)|x, y = -2, –1, 1,2}f(x, y)otherwise,3. Suthe random variables X and Y are indelent and identicallydistributed. Let Z = aX +Y. If the correlation coefficient between X andZ is , then what is the value of the constant a ?

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1. Suppose that X1 and X2 are random variables with zero mean and unit variance. If the correlation coefficient of X1 and X2 is -0.5, then what is the variance of Y =E-k² Xk ? k%3D1

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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Question

Exercises
1. Suppose that X1 and X2 are random variables with zero mean and unit
variance. If the correlation coefficient of X1 and X2 is –0.5, then what is the
variance of Y = =k2Xk ?
Lk=1
2. If the joint density of the random variables X and Y is
if (x, y) E { (x,0), (0, -y)|x, y = -2, –1, 1,2}
f(x, y)
otherwise,
3. Su
the random variables X and Y are inde
lent and identically
distributed. Let Z = aX +Y. If the correlation coefficient between X and
Z is , then what is the value of the constant a ?

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