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# Let X and Y be independent random variables with ?X = 2, ISBN: 9780073401331 38

## Solution for problem 17SE Chapter 2

Statistics for Engineers and Scientists | 4th Edition

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Problem 17SE

Let X and Y be independent random variables with μX = 2, σX = 1, μY = 2, and σY = 3. Find the means and variances of the following quantities.

a. 3X

b. X + Y

c. X-Y

d. 2X + 6Y

Step-by-Step Solution:

Step 1 of 5 :

Given, let X and Y be independent random variables with = 2, = 1, = 2,  and = 3

The claim is to find the mean and variances for the following quantities

3XX + YX - Y2X + 6Y

Step 2 of 5 :

a)

The claim is to find the Mean and Variance for Quantity 3X

Where, = 3 Here, = 2

Therefore, 3 = 3(2)

= 6

And = 3 Where, = 1  = 9(1)

= 9

For the Quantity 3X mean is 6 and variance is 9

Step 3 of 5 :

b)

The claim is to find the Mean and Variance for Quantity X + Y

Where, = + Here, = 2 and = 2

Therefore, = 2 + 2

= 4

And = + Where, = 1 and = 3 + = 1 + 9

= 10

For the Quantity X + Y mean is 4 and variance is 10.

Step 4 of 5

Step 5 of 5

##### ISBN: 9780073401331

The answer to “Let X and Y be independent random variables with ?X = 2, ?X = 1, ?Y = 2, and ?Y = 3. Find the means and variances of the following quantities.a. 3X________________b. X + Y________________c. X-Y________________d. 2X + 6Y” is broken down into a number of easy to follow steps, and 39 words. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. This full solution covers the following key subjects: Find, independent, let, means, quantities. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. The full step-by-step solution to problem: 17SE from chapter: 2 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. Since the solution to 17SE from 2 chapter was answered, more than 265 students have viewed the full step-by-step answer.

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