1. 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
2. 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
3. Refer to Exercise 19.
a. Find µX .
b. Find µY .
c. Find σX .
d. Find σY .
e. Find Cov(X,Y).
f. Find ρX,Y .
