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An insurance company sells both homeowners’ insurance and

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman ISBN: 9780321923271 41

Solution for problem 6E Chapter 4.3

Probability and Statistical Inference | 9th Edition

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Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

Probability and Statistical Inference | 9th Edition

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Problem 6E

PROBLEM 6E

An insurance company sells both homeowners’ insurance and automobile deductible insurance. Let X be the deductible on the homeowners’ insurance and Y the deductible on automobile insurance. Among those who take both types of insurance with this company, we find the following probabilities:

(a) Compute the following probabilities:

P(X = 500), P(Y = 500), P(Y = 500 |X = 500), P(Y = 100 |X = 500).

(b) Compute the means μX, μY, and the variances σ2X,σ2Y .

(c) Compute the conditional means E(X |Y = 100), E(Y |X = 500).

(d) Compute Cov(X,Y).

(e) Find the correlation coefficient, ρ.

Step-by-Step Solution:
Step 1 of 6

Step1 of 6:

Given that X denotes the insurance deductible insurance on the homeowners’ insurance and Y denotes the deductible insurance on automobile insurance. The corresponding probabilities are given.

p1.png

We have to find the required probabilities using the given probabilities.


Step 2 of 6

Chapter 4.3, Problem 6E is Solved
Step 3 of 6

Textbook: Probability and Statistical Inference
Edition: 9
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
ISBN: 9780321923271

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An insurance company sells both homeowners’ insurance and