Explanation Calculation: Suppose the random variables, Y 1 and Y 2 have respective means as E ( Y 1 ) and E ( Y 2 ) , and respective variances as V ( Y 1 ) and V ( Y 2 ) . Denote Cov ( Y 1 , Y 2 ) as the covariance between Y 1 and Y 2 . Then, the formula for the correlation coefficient between the random variables, Y 1 and Y 2 is, ρ = Cov ( Y 1 , Y 2 ) V ( Y 1 ) × V ( Y 2 ) . It is known that the value of ρ must be such that, − 1 ≤ ρ ≤ 1 . Using this property, the range of Cov ( Y 1 , Y 2 ) can be obtained as follows: − 1 ≤ ρ ≤ 1 − 1 ≤ Cov ( Y 1 , Y 2 ) V ( Y 1 ) × V<

Mathematical Statistics with Applications

7th Edition

ISBN: 9780495110811

Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer

Publisher: Cengage Learning

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Chapter 5.7, Problem 98E

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Prove that −V(Y1)×V(Y2)≤Cov(Y1,Y1)≤V(Y1)×V(Y2), to understand how big or small Cov(Y1,Y2) can be.

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Chapter 5.7, Problem 97E

Chapter 5.7, Problem 99E

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Chapter 5 Solutions

Mathematical Statistics with Applications

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Prove that − V ( Y 1 ) × V ( Y 2 ) ≤ Cov ( Y 1 , Y 1 ) ≤ V ( Y 1 ) × V ( Y 2 ) , to understand how big or small Cov ( Y 1 , Y 2 ) can be.

Solution Summary: The author demonstrates that -sqrtV(Y_1)times y2right. The formula for the correlation coefficient between the random variables,

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Prove that −V(Y1)×V(Y2)≤Cov(Y1,Y1)≤V(Y1)×V(Y2), to understand how big or small Cov(Y1,Y2) can be.

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Chapter 5 Solutions