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# If X and Y are independent random variables with means ?X ISBN: 9780073401331 38

## Solution for problem 1E Chapter 2.5

Statistics for Engineers and Scientists | 4th Edition

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Problem 1E

If X and Y are independent random variables with means μX = 9.5 and μγ = 6.8, and standard deviations σX = 0.4 and σγ =0.1, find the means and standard deviations of the following:

a. 3X

b. Y-X

c. X + 4Y

Step-by-Step Solution:

Step 1 of 4:

Here it is given that X and Y are independent random variables.

Also it is given that,

Mean of X, =9.5 and standard deviation of X, =0.4.

Mean of Y, =6.8 and standard deviation of Y, =0.1.

Using these,we have to find the mean and standard deviation of given random variables.

Step 2 of 4:

(a)

Here we have to find the mean and standard deviation of 3X.

We know that                                 mean(aX)=a mean(X)  and

Standard deviation(aX)=|a|standard deviation(X)

Thus,

Mean of 3X , is given by, =3( )

=3(9.5)

=28.5

Standard deviation of 3X , is given by, =|3| =|3|(0.4)

=1.2

Therefore mean of 3X is 28.5 and standard deviation of 3X is 1.2.

Step 3 of 4

Step 4 of 4

##### ISBN: 9780073401331

The full step-by-step solution to problem: 1E from chapter: 2.5 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. The answer to “If X and Y are independent random variables with means ?X = 9.5 and ?? = 6.8, and standard deviations ?X = 0.4 and ?? =0.1, find the means and standard deviations of the following:a. 3X________________b. Y-X________________c. X + 4Y” is broken down into a number of easy to follow steps, and 40 words. Since the solution to 1E from 2.5 chapter was answered, more than 281 students have viewed the full step-by-step answer. This full solution covers the following key subjects: deviations, standard, means, independent, random. 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. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4.

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