Pearson eText for Probability and Statistical Inference -- Instant Access (Pearson+)

10th Edition

ISBN: 9780137538461

Author: Robert Hogg, Elliot Tanis

Publisher: PEARSON+

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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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Pearson eText for Probability and Statistical Inference -- Instant Access (Pearson+)

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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 )