## 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 .

### What is the probability that the parcel was shipped express and arrived the next day?

1.  In a lot of n components, 30% are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective,….

### Given that the test is positive, what is the probability that the person has the disease?

1.  Refer to Exercise 28. Assume that both inspectors inspect every item and that if an item has no flaw, then neither inspector will detect a flaw. a.  Assume that….

### If a man tests negative, what is the probability that he actually has the disease?

1.  Refer to Example 2.26. a.  If a man tests negative, what is the probability that he actually has the disease? b.  For many medical tests, it is standard procedure….