Problem 18SE

Let X and Y be random variables with μX = 1, σX = 2, μY = 3, σY = 1, and ρX,Y = 0.5. Find the means and variances of the following quantities.

a. X + Y

b. X - Y

c. 3X + 2Y

d. 5Y - 2X

Answer :

Step 1 of 1 :

Given,

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

= 0.5

cov(X,Y) = () ( )

= (0.5) (2)(1)

= 1

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

- X + Y

- X - Y

- 3X + 2Y

- 5Y - 2X