1E2E3E4E5E6E7E8E9E10E11E12E13E14E15E16E17E18E19E20E21E22E23E24E25E26E27E28E29E30E31E32E33E34E35E36E37E38E39E40E41E42E43E44E45E46E47E48E49E50E51E52E53E54RE55RE56RE57RE58RE
Show that Cov(XY) = E − EE. Hint: By definition, Cov(X, Y) = E<(X − μX)(Y − μY)>. Expand this product, and apply the rules for expectation (Theorem 3.3.1). Remember that μX = E and μY = E.

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Theorem 3.3.1 (Rules for expectation). Let X and Y be random variables and let c be any real number.

1. E = c (The expected value of any constant is that constant.)

2. E = cE (Constants can be factored from expectations.)

3. E = E + E (The expected value of a sum is equal to the sum of the expected values.)


Show that .

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From the definition 5.2.2, the formula for the covariance is,

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Hence,


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Introduction to Probability and Statistics: Principles and Applications for Engineering and the Computing Sciences | 4th Edition
This is an alternate ISBN. View the primary ISBN for: Introduction to Probability and Statistics 4th Edition Textbook Solutions
This is an alternate ISBN. View the primary ISBN for: Introduction to Probability and Statistics 4th Edition Textbook Solutions
Introduction to Probability and Statistics: Principles and Applications for Engineering and the Computing Sciences (4th Edition) Edit editionSolutions for Chapter 5Problem 24E: Show that Cov(XY) = E − EE. Hint: By definition, Cov(X, Y) = E<(X − μX)(Y − μY)>. Expand this product, and apply the rules for expectation (Theorem 3.3.1). Remember that μX = E and μY = E.Theorem 3.3.1 (Rules for expectation). Let X and Y be random variables and let c be any real number.1. E = c (The expected value of any constant is that constant.)2. E = cE (Constants can be factored from expectations.)3. E = E + E (The expected value of a sum is equal to the sum of the expected values.)…