Find the means and variances of the following quantities.

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 .

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