Elementary Statistics (Text Only)
2nd Edition
ISBN: 9780077836351
Author: Author
Publisher: McGraw Hill
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Chapter 1.3, Problem 26E
Vocabulary and height: A vocabulary test was given to students at an elementary school. The students’ ages
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Question 6. You collect daily data for the stock of a company Z over the past 4 months (i.e. 80
days) and calculate the log-returns (yk)/(-1. You want to build a CRR model for the evolution
of the stock. The expected value and standard deviation of the log-returns are y = 0.06 and
Sy 0.1. The money market interest rate is r = 0.04. Determine the risk-neutral probability of
the model.
Several markets (Japan, Switzerland) introduced negative interest rates on their money market.
In this problem, we will consider an annual interest rate r < 0. We consider a stock modeled
by an N-period CRR model where each period is 1 year (At = 1) and the up and down factors
are u and d.
(a) We consider an American put option with strike price K and expiration T. Prove that if
<0, the optimal strategy is to wait until expiration T to exercise.
We consider an N-period CRR model where each period is 1 year (At = 1), the up factor is
u = 0.1, the down factor is d = e−0.3 and r = 0. We remind you that in the CRR model, the
stock price at time tn is modeled (under P) by
Sta
=
So exp (μtn + σ√AtZn),
where (Zn) is a simple symmetric random walk.
(a) Find the parameters μ and σ for the CRR model described above.
(b) Find P
Ste
So
55/50
€ > 1).
StN
(c) Find lim P
804-N
(d) Determine q. (You can use e- 1 x.)
Ste
(e) Find Q
So
(f) Find lim Q
004-N
StN
So
Chapter 1 Solutions
Elementary Statistics (Text Only)
Ch. 1.1 - In Exercises 7—12, fill in each blank with the...Ch. 1.1 - In Exercises 7—12, fill in each blank with the...Ch. 1.1 - In Exercises 7—12, fill in each blank with the...Ch. 1.1 - In Exercises 7—12, fill in each blank with the...Ch. 1.1 - In Exercises 7—12, fill in each blank with the...Ch. 1.1 - In Exercises 7—12, fill in each blank with the...Ch. 1.1 - In Exercises 13—16, determine whether the...Ch. 1.1 - In Exercises 13—16, determine whether the...Ch. 1.1 - In Exercises 13—16, determine whether the...Ch. 1.1 - In Exercises 13—16, determine whether the...
Ch. 1.1 - In Exercises 17—20, determine whether the number...Ch. 1.1 - In Exercises 17—20, determine whether the number...Ch. 1.1 - In Exercises 17—20, determine whether the number...Ch. 1.1 - In Exercises 17—20, determine whether the number...Ch. 1.1 - Exercises 21—24 refer to the population of...Ch. 1.1 - Exercises 21—24 refer to the population of...Ch. 1.1 - Exercises 21—24 refer to the population of...Ch. 1.1 - Exercises 21—24 refer to the population of...Ch. 1.1 - In Exercises 25—36, identify the kind of sample...Ch. 1.1 - In Exercises 25—36, identify the kind of sample...Ch. 1.1 - In Exercises 25—36, identify the kind of sample...Ch. 1.1 - In Exercises 25—36, identify the kind of sample...Ch. 1.1 - In Exercises 25—36, identify the kind of sample...Ch. 1.1 - In Exercises 25—36, identify the kind of sample...Ch. 1.1 - In Exercises 25—36, identify the kind of sample...Ch. 1.1 - In Exercises 25—36, identify the kind of sample...Ch. 1.1 - In Exercises 25—36, identify the kind of sample...Ch. 1.1 - In Exercises 25—36, identify the kind of sample...Ch. 1.1 - In Exercises 25—36, identify the kind of sample...Ch. 1.1 - In Exercises 25—36, identify the kind of sample...Ch. 1.1 - Computer network: Every third day, a computer...Ch. 1.1 - Smartphone apps: A smartphone app produces a...Ch. 1.1 - Youre giving me a headache: A pharmaceutical...Ch. 1.1 - Pay more for recreation? The director of the...Ch. 1.1 - Voter preferences: A pollster wants to sample 500...Ch. 1.1 - Quality control: Products come off an assembly...Ch. 1.1 - On-site day care: A large company wants to sample...Ch. 1.1 - The tax man cometh: The Internal Revenue Service...Ch. 1.1 - Draw a sample: Imagine that you are asked to...Ch. 1.1 - A systematic sample is a cluster sample: Explain...Ch. 1.2 - In Exercises 5—10, fill in each blank with the...Ch. 1.2 - In Exercises 5—10, fill in each blank with the...Ch. 1.2 - In Exercises 5—10, fill in each blank with the...Ch. 1.2 - In Exercises 5—10, fill in each blank with the...Ch. 1.2 - In Exercises 5—10, fill in each blank with the...Ch. 1.2 - In Exercises 5—10, fill in each blank with the...Ch. 1.2 - In Exercises 11—14, determine whether the...Ch. 1.2 - In Exercises 11—14, determine whether the...Ch. 1.2 - In Exercises 11—14, determine whether the...Ch. 1.2 - In Exercises 11—14, determine whether the...Ch. 1.2 - In Exercises 15—24, determine whether the data...Ch. 1.2 - In Exercises 15—24, determine whether the data...Ch. 1.2 - In Exercises 15—24, determine whether the data...Ch. 1.2 - In Exercises 15—24, determine whether the data...Ch. 1.2 - In Exercises 15—24, determine whether the data...Ch. 1.2 - In Exercises 15—24, determine whether the data...Ch. 1.2 - In Exercises 15—24, determine whether the data...Ch. 1.2 - In Exercises 15—24, determine whether the data...Ch. 1.2 - In Exercises 15—24, determine whether the data...Ch. 1.2 - In Exercises 15—24, determine whether the data...Ch. 1.2 - In Exercises 25—32, determine whether the data...Ch. 1.2 - In Exercises 25—32, determine whether the data...Ch. 1.2 - In Exercises 25—32, determine whether the data...Ch. 1.2 - In Exercises 25—32, determine whether the data...Ch. 1.2 - In Exercises 25—32, determine whether the data...Ch. 1.2 - In Exercises 25—32, determine whether the data...Ch. 1.2 - In Exercises 25—32, determine whether the data...Ch. 1.2 - In Exercises 25—32, determine whether the data...Ch. 1.2 - In Exercises 33—40, determine whether the data...Ch. 1.2 - In Exercises 33—40, determine whether the data...Ch. 1.2 - In Exercises 33—40, determine whether the data...Ch. 1.2 - In Exercises 33—40, determine whether the data...Ch. 1.2 - In Exercises 33—40, determine whether the data...Ch. 1.2 - In Exercises 33—40, determine whether the data...Ch. 1.2 - In Exercises 33—40, determine whether the data...Ch. 1.2 - In Exercises 33—40, determine whether the data...Ch. 1.2 - Prob. 41ECh. 1.2 - Prob. 42ECh. 1.2 - Prob. 43ECh. 1.2 - Prob. 44ECh. 1.2 - Read any good books lately? According to time...Ch. 1.2 - Prob. 46ECh. 1.2 - Prob. 47ECh. 1.2 - Prob. 48ECh. 1.2 - What do the numbers mean?A survey is administered...Ch. 1.3 - In Exercises 5—10, fill in each blank with the...Ch. 1.3 - In Exercises 5—10, fill in each blank with the...Ch. 1.3 - In Exercises 5—10, fill in each blank with the...Ch. 1.3 - In Exercises 5—10, fill in each blank with the...Ch. 1.3 - In Exercises 5—10, fill in each blank with the...Ch. 1.3 - In Exercises 5—10, fill in each blank with the...Ch. 1.3 - In Exercise 11—16, determine whether the...Ch. 1.3 - In Exercise 11—16, determine whether the...Ch. 1.3 - In Exercise 11—16, determine whether the...Ch. 1.3 - In Exercise 11—16, determine whether the...Ch. 1.3 - In Exercise 11—16, determine whether the...Ch. 1.3 - In Exercise 11—16, determine whether the...Ch. 1.3 - To determine the effectiveness of a new pain...Ch. 1.3 - A medical researcher wants to determine whether...Ch. 1.3 - A medical researcher wants to determine whether...Ch. 1.3 - An agricultural scientist wants to determine the...Ch. 1.3 - Air pollution and colds: A scientist wants to...Ch. 1.3 - Cold medications: A scientist wants to determine...Ch. 1.3 - Taxicabs and crime: A sociologist discovered that...Ch. 1.3 - Recovering from heart attacks: In a study of...Ch. 1.3 - Eat your vegetables: In an observational study,...Ch. 1.3 - Vocabulary and height: A vocabulary test was given...Ch. 1.3 - Secondhand smoke: A recent study compared the...Ch. 1.3 - Pollution in China: In a recent study, Z. Zhao and...Ch. 1.3 - The Salk Vaccine Trial: In 1954, the first vaccine...Ch. 1.3 - Another Salk Vaccine Trial: Another study of the...Ch. 1.4 - In Exercises 3—5, fill in each blank with the...Ch. 1.4 - In Exercises 3—5, fill in each blank with the...Ch. 1.4 - In Exercises 3—5, fill in each blank with the...Ch. 1.4 - In Exercises 6—8, determine whether the...Ch. 1.4 - In Exercises 6—8, determine whether the...Ch. 1.4 - In Exercises 6—8, determine whether the...Ch. 1.4 - In Exercises 9—16, specify the type of bias...Ch. 1.4 - In Exercises 9—16, specify the type of bias...Ch. 1.4 - In Exercises 9—16, specify the type of bias...Ch. 1.4 - In Exercises 9—16, specify the type of bias...Ch. 1.4 - In Exercises 9—16, specify the type of bias...Ch. 1.4 - In Exercises 9—16, specify the type of bias...Ch. 1.4 - In Exercises 9—16, specify the type of bias...Ch. 1.4 - In Exercises 9—16, specify the type of bias...Ch. 1.4 - Nuclear power, anyone? In a survey conducted by...Ch. 1.4 - Whos calling, please? Random-digit dialing is a...Ch. 1.4 - Whos calling, please? Many polls are conducted...Ch. 1.4 - Order of choices: When multiple-choice questions...Ch. 1.4 - Literary Digest poll: In the 1936 presidential...Ch. 1 - Provide an example of a qualitative variable and...Ch. 1 - Is the name of your favorite author a qualitative...Ch. 1 - Prob. 3CQCh. 1 - Prob. 4CQCh. 1 - True or false: Ideally, a sample should represent...Ch. 1 - Prob. 6CQCh. 1 - Prob. 7CQCh. 1 - Prob. 8CQCh. 1 - Prob. 9CQCh. 1 - Prob. 10CQCh. 1 - Prob. 11CQCh. 1 - Prob. 12CQCh. 1 - In analyzing the course grades of students in an...Ch. 1 - Prob. 14CQCh. 1 - Prob. 15CQCh. 1 - Prob. 1RECh. 1 - Prob. 2RECh. 1 - Prob. 3RECh. 1 - Prob. 4RECh. 1 - In Exercises 5—8, identify the kind of sample...Ch. 1 - Prob. 6RECh. 1 - Prob. 7RECh. 1 - Prob. 8RECh. 1 - Fluoride and tooth decay: Researchers examine the...Ch. 1 - Better gas mileage: A taxi company in a large city...Ch. 1 - Prob. 11RECh. 1 - Prob. 12RECh. 1 - Prob. 13RECh. 1 - Prob. 14RECh. 1 - Prob. 15RECh. 1 - Describe the difference between a stratified...Ch. 1 - Prob. 2WAICh. 1 - Describe circumstances under which each of the...Ch. 1 - Suppose that you were asked to collect some...Ch. 1 - Prob. 5WAICh. 1 - What are the primary differences between a...Ch. 1 - What are the advantages of a double-blind study?...Ch. 1 - Prob. 8WAICh. 1 - Prob. 9WAICh. 1 - Air pollution is a serious problem in many places....Ch. 1 - Prob. 2CSCh. 1 - Air pollution is a serious problem in many places....Ch. 1 - Air pollution is a serious problem in many places....Ch. 1 - Air pollution is a serious problem in many places....Ch. 1 - Air pollution is a serious problem in many places....Ch. 1 - Is there a large difference between the percentage...Ch. 1 - Explain why the percentage of high-exposure people...Ch. 1 - Explain why the percentage of low-exposure people...Ch. 1 - As the weather sets warmer. PM goes down because...Ch. 1 - It is generally the case in epidemiologic studies...Ch. 1 - Rather than send out questionnaires, the...
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- In this problem, we consider a 3-period stock market model with evolution given in Fig. 1 below. Each period corresponds to one year. The interest rate is r = 0%. 16 22 28 12 16 12 8 4 2 time Figure 1: Stock evolution for Problem 1. (a) A colleague notices that in the model above, a movement up-down leads to the same value as a movement down-up. He concludes that the model is a CRR model. Is your colleague correct? (Explain your answer.) (b) We consider a European put with strike price K = 10 and expiration T = 3 years. Find the price of this option at time 0. Provide the replicating portfolio for the first period. (c) In addition to the call above, we also consider a European call with strike price K = 10 and expiration T = 3 years. Which one has the highest price? (It is not necessary to provide the price of the call.) (d) We now assume a yearly interest rate r = 25%. We consider a Bermudan put option with strike price K = 10. It works like a standard put, but you can exercise it…arrow_forwardIn this problem, we consider a 2-period stock market model with evolution given in Fig. 1 below. Each period corresponds to one year (At = 1). The yearly interest rate is r = 1/3 = 33%. This model is a CRR model. 25 15 9 10 6 4 time Figure 1: Stock evolution for Problem 1. (a) Find the values of up and down factors u and d, and the risk-neutral probability q. (b) We consider a European put with strike price K the price of this option at time 0. == 16 and expiration T = 2 years. Find (c) Provide the number of shares of stock that the replicating portfolio contains at each pos- sible position. (d) You find this option available on the market for $2. What do you do? (Short answer.) (e) We consider an American put with strike price K = 16 and expiration T = 2 years. Find the price of this option at time 0 and describe the optimal exercising strategy. (f) We consider an American call with strike price K ○ = 16 and expiration T = 2 years. Find the price of this option at time 0 and describe…arrow_forward2.2, 13.2-13.3) question: 5 point(s) possible ubmit test The accompanying table contains the data for the amounts (in oz) in cans of a certain soda. The cans are labeled to indicate that the contents are 20 oz of soda. Use the sign test and 0.05 significance level to test the claim that cans of this soda are filled so that the median amount is 20 oz. If the median is not 20 oz, are consumers being cheated? Click the icon to view the data. What are the null and alternative hypotheses? OA. Ho: Medi More Info H₁: Medi OC. Ho: Medi H₁: Medi Volume (in ounces) 20.3 20.1 20.4 Find the test stat 20.1 20.5 20.1 20.1 19.9 20.1 Test statistic = 20.2 20.3 20.3 20.1 20.4 20.5 Find the P-value 19.7 20.2 20.4 20.1 20.2 20.2 P-value= (R 19.9 20.1 20.5 20.4 20.1 20.4 Determine the p 20.1 20.3 20.4 20.2 20.3 20.4 Since the P-valu 19.9 20.2 19.9 Print Done 20 oz 20 oz 20 oz 20 oz ce that the consumers are being cheated.arrow_forward
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