Probability And Statistical Inference (10th Edition)

10th Edition

ISBN: 9780135189399

Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

Publisher: PEARSON

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Textbook Question

Chapter 4.5, Problem 4E

Let X and Y have a bivariate normal distribution μ X = 70 , σ X 2 = 100 , μ Y = 80 , σ Y 2 = 169 , and ρ = 5 13 .

Find

(a) E ( Y | X = 76 ) .

(b) V a r ( Y | X = 76 ) .

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Chapter 4.5, Problem 3E

Chapter 4.5, Problem 5E

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Chapter 4 Solutions

Probability And Statistical Inference (10th Edition)

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Let X and Y have a bivariate normal distribution μ X = 70 , σ X 2 = 100 , μ Y = 80 , σ Y 2 = 169 , and ρ = 5 13 . Find (a) E ( Y | X = 76 ) . (b) V a r ( Y | X = 76 ) . (c) P ( Y ≤ 86 | X = 76 ) .

Solution Summary: The author explains that the required conditional variance of Y, given X=x, is 83.

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Chapter 4 Solutions