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Let X, Y, and Z be jointly distributed random variables.

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 28E Chapter 2.6

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 28E

Let X, Y, and Z be jointly distributed random variables. Prove that Cov(X + Y, Z) = Cov(X, Z) + Cov(Y, Z). (Hint: Use Equation 2.69.)

Step-by-Step Solution:

Solution :

Step 1 of 1:

Given  X,Y, and Z be the jointly distributed random variable.

Our goal is :

a). We need to prove that Cov(X+Y,Z)=Cov(X,Z)+Cov(Y,Z).

a).

Now we need to prove that Cov(X+Y,Z)=Cov(X,Z)+Cov(Y,Z).

Here

Here we multiply X and Y by Z.

Then

and

So

Therefore


 

 

Step 2 of 1

Chapter 2.6, Problem 28E is Solved
Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. The answer to “Let X, Y, and Z be jointly distributed random variables. Prove that Cov(X + Y, Z) = Cov(X, Z) + Cov(Y, Z). (Hint: Use Equation 2.69.)” is broken down into a number of easy to follow steps, and 26 words. Since the solution to 28E from 2.6 chapter was answered, more than 280 students have viewed the full step-by-step answer. This full solution covers the following key subjects: cov, let, equation, hint, jointly. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. The full step-by-step solution to problem: 28E from chapter: 2.6 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM.

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Let X, Y, and Z be jointly distributed random variables.