Homework #3
(Due date: 2-May)
DeGroot Exercises
4.1.13
A stock currently sells for $110 per share. Let the price of the stock at the end of a oneyear period be X , which will take one of the values $100 or $300. Suppose that you have
the option to buy sha

Answers to PS#6
1. b
2. a
3. b
4. c
5. a
6. a
7. a
8. e
9. b
10.
5-12. a.
E(rP) = (0.3 6%) + (0.7 15%) = 12.30% per year
P = 0.7 25% = 17.5% per year
b.
Investment
c.
Security
Proportions
T-Bills
Stock A
0.7 27% =
30.0%
18.9%
Stock B
0.7 33% =
23.1%
Stock

Answers to PS #1
1. e
2. d
3. b
4. b
5. e
6. b
7. a
8. c
9. b
10. c
11. Percentage Margin (PM)
= [Market Value of Securities - Loan] / Market Value
a. PM = (100 x $40 - 2,000) / 100 x $40 = 50%
b. PM = (100 x $60 - 2,000) / 100 x $60 = 66.7%
PM = (100 x $

Answers to PS #4
1. a
2. a
11. c
3. c
12. a
4. c
13. b
5. e
6. e
7. b
8. c
9. c
10. c
14. A&C is dominated by B&C.
15.
a. E(rp) = (0.3)(10) + (0.7)(20) = 17%
Var(rp) = (0.3)2(20)2 + (0.7)2(30)2 + 2x(0.3)(0.7)(0.4)(20)(30) = 578 (%)2
p = (578)1/2 = 24%
b.

Answers to PS #3
1. b
2. a
3. c
4. d
5. a
6. d
7. c
8. c
9.
a. Index0 = (90+50+100)/3 = 80; Index1 = (95+45+110)/3 = 83.33
Rate of Return = (83.88-80)/80 = 4.16%
b. It must be adjusted downward.
(95+45+55)/divisor = (95+45+110)/3 = 83.3 => divisor = 2.34

Homework #5
(Due date: 7-June)
Montgomery Exercises
9-10
The heat evolved in calories per gram of a cement mixture is approximately normally
distributed. The mean is thought to be 100, and the standard deviation is 2. You wish to
test H 0 : = 100 versus H

Homework #4
(Due date: 30-May)
Montgomery Exercises
7-4
Suppose that samples of size n = 25 are selected at random from a normal population
with mean 100 and standard deviation 10. What is the probability that the sample mean
falls in the interval from X

Homework #1
(Due date: 21-March)
DeGroot Exercises
1.5.4
If the probability that student A will fail a certain statistics examination is 0.5, the probability
that student B will fail the examination is 0.2, and the probability that both student A and
stud

Homework #2
(Due date: 4-April)
DeGroot Exercises
3.1.6
Suppose that a random variable X has the binomial distribution with parameters n =
15 and p = 0.5. Find Pr( X 6 ).
3.1.8
If 10 percent of the balls in a certain box are red, and if 20 balls are selec

Answers to PS#5
1. c
2. e
3. d
4. d
5. c
6. b
7. b
8. e
9. c
10.
Q5.
a. Subscript OP refers to the original portfolio, ABC to the new stock, and NP to the new portfolio.
i.
E(rNP) = wOP E(rOP ) + wABC E(rABC ) = (0.9 0.67) + (0.1 1.25) = 0.728%
ii.
Cov =