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:
c. X + 4Y
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:
Here we have to find the mean and standard deviation of 3X.
We know that mean(aX)=amean(X) and
Standard deviation(aX)=|a|standard deviation(X)
Mean of 3X , is given by,
Standard deviation of 3X , is given by,
Therefore mean of 3X is 28.5 and standard deviation of 3X is 1.2.
Textbook: Statistics for Engineers and Scientists
Author: William Navidi
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.