Probability and Statistical Inference (9th Edition)

9th Edition

ISBN: 9780321923271

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

Publisher: PEARSON

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Textbook Question

Chapter 4.5, Problem 3E

Let X and Y have a bivariate normal distribution with parameters μ x = 2.8 , μ y = 110 , σ x 2 = 0.16 , σ y 2 = 100 , and ρ = 0.6 .

Compute

(a) P ( 108 < Y < 126 ) .

(b) P ( 108 < Y < 126 | X = 3.2 )

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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Chapter 4.5, Problem 2E

Chapter 4.5, Problem 4E

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Let X and Y have a bivariate normal distribution with parameters μ x = 2.8 , μ y = 110 , σ x 2 = 0.16 , σ y 2 = 100 , and ρ = 0.6 . Compute (a) P ( 108 &lt; Y &lt; 126 ) . (b) P ( 108 &lt; Y &lt; 126 | X = 3.2 )

Solution Summary: The author calculates the conditional mean and variance as follows: P(106Y124|X=3.2)

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Chapter 4 Solutions

Let X and Y have a bivariate normal distribution with parameters μ x = 2.8 , μ y = 110 , σ x 2 = 0.16 , σ y 2 = 100 , and ρ = 0.6 . Compute (a) P ( 108 < Y < 126 ) . (b) P ( 108 < Y < 126 | X = 3.2 )