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

Answer :

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 + 6YStep 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.