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Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 2.6 - Problem 28e
Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 2.6 - Problem 28e

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

ISBN: 9780073401331 38

## Solution for problem 28E Chapter 2.6

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

##### 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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