Pearson eText for An Introduction to Mathematical Statistics and Its Applications -- Instant Access (Pearson+)
6th Edition
ISBN: 9780137549375
Author: Richard Larsen, Morris Marx
Publisher: PEARSON+
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Chapter 10.4, Problem 1Q
A public policy polling group is investigating whether people living in the same household tend to make independent political choices. They select two hundred home where exactly three voters live. The residents are asked separately for their opinion (“yes” or “no”) on a city charter amendment. If their opinions are formed in-dependently, Do an appropriate goodness-of-fit test on the data below. Let
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Question 2. An American option on a stock has payoff given by F = f(St) when it is exercised
at time t. We know that the function f is convex. A person claims that because of convexity,
it is optimal to exercise at expiration T. Do you agree with them?
Question 4. We consider a CRR model with So == 5 and up and down factors u = 1.03 and
d = 0.96. We consider the interest rate r = 4% (over one period). Is this a suitable CRR
model? (Explain your answer.)
Question 3. We want to price a put option with strike price K and expiration T. Two financial
advisors estimate the parameters with two different statistical methods: they obtain the same
return rate μ, the same volatility σ, but the first advisor has interest r₁ and the second advisor
has interest rate r2 (r1>r2). They both use a CRR model with the same number of periods to
price the option. Which advisor will get the larger price? (Explain your answer.)
Chapter 10 Solutions
Pearson eText for An Introduction to Mathematical Statistics and Its Applications -- Instant Access (Pearson+)
Ch. 10.2 - The Advanced Placement Program allows high school...Ch. 10.2 - In Mendels classical experiments with peas, he...Ch. 10.2 - Prob. 3QCh. 10.2 - An army enlistment officer categorizes potential...Ch. 10.2 - A disgruntled Anchorage bush pilot, upset because...Ch. 10.2 - Based on his performance so far this season, a...Ch. 10.2 - Suppose that a random sample of fifty observations...Ch. 10.2 - Let the vector of random variables (X1,X2,X3) have...Ch. 10.2 - Prob. 9QCh. 10.2 - Prob. 10Q
Ch. 10.3 - Verify the following identity concerning the...Ch. 10.3 - One hundred unordered samples of size 2 are drawn...Ch. 10.3 - Prob. 3QCh. 10.3 - Show that the common belief in the propensity of...Ch. 10.3 - Prob. 5QCh. 10.3 - A number of reports in the medical literature...Ch. 10.3 - In a move that shocked candy traditionalists at...Ch. 10.3 - Test at the 0.10 level whether World Series...Ch. 10.3 - Records Kept at an eastern racetrack showed the...Ch. 10.3 - Prob. 10QCh. 10.3 - Prob. 11QCh. 10.3 - The man () and standard deviation () of pregnancy...Ch. 10.4 - A public policy polling group is investigating...Ch. 10.4 - From 1837 to 1932, the U.S. Supreme Court had...Ch. 10.4 - Prob. 3QCh. 10.4 - Carry out the details for goodness-of-fit test on...Ch. 10.4 - Prob. 5QCh. 10.4 - Do a goodness-of-fit test for normality on the SAT...Ch. 10.4 - A sociologist is studying various aspects of the...Ch. 10.4 - In theory, Monte Carlo studies rely on computers...Ch. 10.4 - Because it satisfies all the assumptions implicit...Ch. 10.4 - In American football a turnover is defined as a...Ch. 10.4 - Prob. 11QCh. 10.4 - To raise money for a new rectory, the members of a...Ch. 10.4 - Prob. 14QCh. 10.5 - While there are a number of diet and physical...Ch. 10.5 - Prob. 2QCh. 10.5 - A total of 1154 girls attending a public high...Ch. 10.5 - Recall the rubella/birth defect study described in...Ch. 10.5 - Research has suggested that regular use of aspirin...Ch. 10.5 - High blood pressure is known to be one of the...Ch. 10.5 - The following data were collected as part of a...Ch. 10.5 - A university conducted a study to assess...Ch. 10.5 - Some studies have suggested that pilots have an...Ch. 10.5 - Students elect to take Calculus I in different...
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- 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 Soarrow_forwardIn 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_forward
- 2.2, 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_forwardT Teenage obesity (O), and weekly fast-food meals (F), among some selected Mississippi teenagers are: Name Obesity (lbs) # of Fast-foods per week Josh 185 10 Karl 172 8 Terry 168 9 Kamie Andy 204 154 12 6 (a) Compute the variance of Obesity, s²o, and the variance of fast-food meals, s², of this data. [Must show full work]. (b) Compute the Correlation Coefficient between O and F. [Must show full work]. (c) Find the Coefficient of Determination between O and F. [Must show full work]. (d) Obtain the Regression equation of this data. [Must show full work]. (e) Interpret your answers in (b), (c), and (d). (Full explanations required). Edit View Insert Format Tools Tablearrow_forwardThe average miles per gallon for a sample of 40 cars of model SX last year was 32.1, with a population standard deviation of 3.8. A sample of 40 cars from this year’s model SX has an average of 35.2 mpg, with a population standard deviation of 5.4. Find a 99 percent confidence interval for the difference in average mpg for this car brand (this year’s model minus last year’s).Find a 99 percent confidence interval for the difference in average mpg for last year’s model minus this year’s. What does the negative difference mean?arrow_forward
- A special interest group reports a tiny margin of error (plus or minus 0.04 percent) for its online survey based on 50,000 responses. Is the margin of error legitimate? (Assume that the group’s math is correct.)arrow_forwardSuppose that 73 percent of a sample of 1,000 U.S. college students drive a used car as opposed to a new car or no car at all. Find an 80 percent confidence interval for the percentage of all U.S. college students who drive a used car.What sample size would cut this margin of error in half?arrow_forwardYou want to compare the average number of tines on the antlers of male deer in two nearby metro parks. A sample of 30 deer from the first park shows an average of 5 tines with a population standard deviation of 3. A sample of 35 deer from the second park shows an average of 6 tines with a population standard deviation of 3.2. Find a 95 percent confidence interval for the difference in average number of tines for all male deer in the two metro parks (second park minus first park).Do the parks’ deer populations differ in average size of deer antlers?arrow_forward
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