3.5.8. Let X and Y have a bivariate normal distribution with parameters u1 20, µ2 = 40, o? = 9, o? = 4, and p = 0.6. Find the shortest interval for which 0.90 is the conditional probability that Y is in the interval, given that X 22. %3D %3D %3D

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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3.5.8. Let X and Y have a bivariate normal distribution with parameters u1 =
20, µ2 = 40, of = 9, o = 4, and p = 0.6. Find the shortest interval for which 0.90
is the conditional probability that Y is in the interval, given that X 22.
3.5.9. Say the correlation coefficient between the heights of husbands and wives is
0.70 and the mean male height is 5 feet 10 inches with standard deviation 2 inches,
and the mean female height is 5 feet 4 inches with standard deviation 1 inches.
Assuming a bivariate normal distribution, what is the best guess of the height of
a woman whose husband's height is 6 feet? Find a 95% prediction interval for her
height.
Transcribed Image Text:3.5.8. Let X and Y have a bivariate normal distribution with parameters u1 = 20, µ2 = 40, of = 9, o = 4, and p = 0.6. Find the shortest interval for which 0.90 is the conditional probability that Y is in the interval, given that X 22. 3.5.9. Say the correlation coefficient between the heights of husbands and wives is 0.70 and the mean male height is 5 feet 10 inches with standard deviation 2 inches, and the mean female height is 5 feet 4 inches with standard deviation 1 inches. Assuming a bivariate normal distribution, what is the best guess of the height of a woman whose husband's height is 6 feet? Find a 95% prediction interval for her height.
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