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 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)=amean(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.