Statistics: Informed Decisions Using Data (5th Edition)
5th Edition
ISBN: 9780134133539
Author: Michael Sullivan III
Publisher: PEARSON
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Chapter 9.5, Problem 19AYU
(a)
To determine
To simulate: A sample of size 12 for a normal population.
(b)
To determine
To construct: The confidence interval for average IQ by t-distribution.
(c)
To determine
To compute: Bootstrap samples and the individual mean of computed samples.
(d)
To determine
Estimated value of the standard error of mean for samples of part (c).
To determine
To compare: The standard error obtained above with the theoretical standard error.
(e)
To determine
To construct: The confidence interval for average IQ for the bootstrap samples obtained in part (c).
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Students have asked these similar questions
In this problem, we consider a Brownian motion (W+) t≥0. We consider a stock model (St)t>0
given (under the measure P) by
d.St 0.03 St dt + 0.2 St dwt,
with So 2. We assume that the interest rate is r = 0.06. The purpose of this problem is to
price an option on this stock (which we name cubic put). This option is European-type, with
maturity 3 months (i.e. T = 0.25 years), and payoff given by
F = (8-5)+
(a) Write the Stochastic Differential Equation satisfied by (St) under the risk-neutral measure
Q. (You don't need to prove it, simply give the answer.)
(b) Give the price of a regular European put on (St) with maturity 3 months and strike K = 2.
(c) Let X =
S. Find the Stochastic Differential Equation satisfied by the process (Xt)
under the measure Q.
(d) Find an explicit expression for X₁ = S3 under measure Q.
(e) Using the results above, find the price of the cubic put option mentioned above.
(f) Is the price in (e) the same as in question (b)? (Explain why.)
Problem 4. Margrabe formula and the Greeks (20 pts)
In the homework, we determined the Margrabe formula for the price of an option allowing you to
swap an x-stock for a y-stock at time T. For stocks with initial values xo, yo, common volatility
σ and correlation p, the formula was given by
Fo=yo (d+)-x0Þ(d_),
where
In (±²
Ꭲ
d+
õ√T
and
σ = σ√√√2(1 - p).
дго
(a) We want to determine a "Greek" for ỡ on the option: find a formula for
θα
(b) Is
дго
θα
positive or negative?
(c) We consider a situation in which the correlation p between the two stocks increases: what
can you say about the price Fo?
(d) Assume that yo< xo and p = 1. What is the price of the option?
We consider a 4-dimensional stock price model given (under P) by
dẴ₁ = µ· Xt dt + йt · ΣdŴt
where (W) is an n-dimensional Brownian motion,
π = (0.02, 0.01, -0.02, 0.05),
0.2
0
0
0
0.3
0.4
0
0
Σ=
-0.1
-4a За
0
0.2
0.4 -0.1 0.2)
and a E R. We assume that ☑0 = (1, 1, 1, 1) and that the interest rate on the market is r = 0.02.
(a) Give a condition on a that would make stock #3 be the one with largest volatility.
(b) Find the diversification coefficient for this portfolio as a function of a.
(c) Determine the maximum diversification coefficient d that you could reach by varying the
value of a?
2
Chapter 9 Solutions
Statistics: Informed Decisions Using Data (5th Edition)
Ch. 9.1 - 1. A _______ ________ is the value of a statistic...Ch. 9.1 - 2. The ______ ____ _______ represents the expected...Ch. 9.1 - 3. True or False: A 95% confidence interval for a...Ch. 9.1 - 4. The value represents the _______ _______ of...Ch. 9.1 - 5. As the level of confidence of a confidence...Ch. 9.1 - 6. As the sample size used to obtain a confidence...Ch. 9.1 - In Problems 7–10, determine the critical value...Ch. 9.1 - In Problems 7–10, determine the critical value...Ch. 9.1 - In Problems 7–10, determine the critical value...Ch. 9.1 - In Problems 7–10, determine the critical value...
Ch. 9.1 - Prob. 11AYUCh. 9.1 - In Problems 11–14, determine the point estimate of...Ch. 9.1 - In Problems 11–14, determine the point estimate of...Ch. 9.1 - Prob. 14AYUCh. 9.1 - In Problems 15–20, construct a confidence interval...Ch. 9.1 - In Problems 15–20, construct a confidence interval...Ch. 9.1 - In Problems 15–20, construct a confidence interval...Ch. 9.1 - In Problems 15–20, construct a confidence interval...Ch. 9.1 - Prob. 19AYUCh. 9.1 - Prob. 20AYUCh. 9.1 - Prob. 21AYUCh. 9.1 - 22. You Explain It! Superstition A USA...Ch. 9.1 - Prob. 23AYUCh. 9.1 - Prob. 24AYUCh. 9.1 - NW 25. Giving Blood A survey of 2306 adult...Ch. 9.1 - 26. Saving for Retirement? A Retirement Confidence...Ch. 9.1 - Prob. 27AYUCh. 9.1 - 28. Family Values In a USA Today/Gallup poll, 768...Ch. 9.1 - Prob. 29AYUCh. 9.1 - 30. Reading In a survey of 700 community college...Ch. 9.1 - Prob. 31AYUCh. 9.1 - 32. Deficit Reduction The Sullivan Statistics...Ch. 9.1 - Prob. 33AYUCh. 9.1 - Prob. 34AYUCh. 9.1 - NW 35. High-Speed Internet Access A researcher...Ch. 9.1 - 36. Home Ownership An urban economist wishes to...Ch. 9.1 - 37. A Penny for Your Thoughts A researcher for the...Ch. 9.1 - Prob. 38AYUCh. 9.1 - Prob. 39AYUCh. 9.1 - Prob. 40AYUCh. 9.1 - Prob. 41AYUCh. 9.1 - Prob. 42AYUCh. 9.1 - Prob. 43AYUCh. 9.1 - 44. Simulation – When Model Requirements Fail A...Ch. 9.1 - 45. Cauliflower? Jane wants to estimate the...Ch. 9.1 - 46. Walk to Work Alan wants to estimate the...Ch. 9.1 - 47. Putting It Together: Hand Washing The American...Ch. 9.1 - Prob. 48AYUCh. 9.1 - Prob. 49AYUCh. 9.1 - Prob. 50AYUCh. 9.1 - Prob. 51AYUCh. 9.1 - Prob. 52AYUCh. 9.1 - Prob. 53AYUCh. 9.1 - 54. The 114th Congress of the United States of...Ch. 9.2 - 1. As the number of degrees of freedom in the...Ch. 9.2 - 2. True or False: The t-distribution is centered...Ch. 9.2 - 3. The notation tα is the t-value such that the...Ch. 9.2 - 4. True or False: The value of t0.10 with 5...Ch. 9.2 - 5. True or False: To construct a confidence...Ch. 9.2 - 6. The procedure for constructing a confidence...Ch. 9.2 - 7. (a) Find the t-value such that the area in the...Ch. 9.2 - Prob. 8AYUCh. 9.2 - Prob. 9AYUCh. 9.2 - Prob. 10AYUCh. 9.2 - In Problems 9–12, a simple random sample of size n...Ch. 9.2 - Prob. 12AYUCh. 9.2 - In Problems 13–16, determine the point estimate of...Ch. 9.2 - Prob. 14AYUCh. 9.2 - In Problems 13–16, determine the point estimate of...Ch. 9.2 - Prob. 16AYUCh. 9.2 - Prob. 17AYUCh. 9.2 - Prob. 18AYUCh. 9.2 - Prob. 19AYUCh. 9.2 - 20. A simple random sample of size n is drawn. The...Ch. 9.2 - Prob. 21AYUCh. 9.2 - Prob. 22AYUCh. 9.2 - Prob. 23AYUCh. 9.2 - Prob. 24AYUCh. 9.2 - Prob. 25AYUCh. 9.2 - Prob. 26AYUCh. 9.2 - 27. Blood Alcohol Concentration A random sample of...Ch. 9.2 - 28. Hungry or Thirsty? How much time do Americans...Ch. 9.2 - 29. Tootsie Pops A Tootsie Pop is a sucker with a...Ch. 9.2 - 30. How Much Do You Read? A recent Gallup poll...Ch. 9.2 - Prob. 31AYUCh. 9.2 - Prob. 32AYUCh. 9.2 - Prob. 33AYUCh. 9.2 - Prob. 34AYUCh. 9.2 - Prob. 35AYUCh. 9.2 - Prob. 36AYUCh. 9.2 - Prob. 37AYUCh. 9.2 - Prob. 38AYUCh. 9.2 - Prob. 39AYUCh. 9.2 - 40. Sexual Relations A question on the General...Ch. 9.2 - 41. Sample Size Dr. Paul Oswiecmiski wants to...Ch. 9.2 - 42. Sample Size Dr. Paul Oswiecmiski wants to...Ch. 9.2 - Prob. 43AYUCh. 9.2 - 44. Television A researcher wanted to determine...Ch. 9.2 - Prob. 45AYUCh. 9.2 - Prob. 46AYUCh. 9.2 - Prob. 47AYUCh. 9.2 - Prob. 48AYUCh. 9.2 - Prob. 49AYUCh. 9.2 - Prob. 50AYUCh. 9.2 - Prob. 51AYUCh. 9.2 - Prob. 52AYUCh. 9.2 - Prob. 53AYUCh. 9.2 - Prob. 54AYUCh. 9.2 - Prob. 55AYUCh. 9.2 - Prob. 56AYUCh. 9.3 - 1. True or False: The chi-square distribution is...Ch. 9.3 - 2. True or False: The shape of the chi-square...Ch. 9.3 - 3. True or False: To construct a confidence...Ch. 9.3 - 4. True or False: A confidence interval for a...Ch. 9.3 - In Problems 5–8, find the critical values and ...Ch. 9.3 - In Problems 5–8, find the critical values and ...Ch. 9.3 - In Problems 5–8, find the critical values and ...Ch. 9.3 - In Problems 5–8, find the critical values and ...Ch. 9.3 -
9. A simple random sample of size n is drawn from...Ch. 9.3 - Prob. 10AYUCh. 9.3 - 11. pH of Rain The following data represent the pH...Ch. 9.3 - 12. Travel Taxes Travelers pay taxes for flying,...Ch. 9.3 - 13. Crash Test Results The following data...Ch. 9.3 - 14. Crawling Babies The data in the next column...Ch. 9.3 - 15. Peanuts A jar of peanuts is supposed to have...Ch. 9.3 - Prob. 16AYUCh. 9.3 - 17. Critical Values Sir R. A. Fisher, a famous...Ch. 9.4 - 1. For what type of variable does it make sense to...Ch. 9.4 - Prob. 2AYUCh. 9.4 - Prob. 3AYUCh. 9.4 - Prob. 4AYUCh. 9.4 - In Problems 5–12, construct the appropriate...Ch. 9.4 - Prob. 6AYUCh. 9.4 - Prob. 7AYUCh. 9.4 - Prob. 8AYUCh. 9.4 - Prob. 9AYUCh. 9.4 - Prob. 10AYUCh. 9.4 - Prob. 11AYUCh. 9.4 - Prob. 12AYUCh. 9.4 - Prob. 13AYUCh. 9.4 - Prob. 14AYUCh. 9.4 - Prob. 15AYUCh. 9.4 - Prob. 16AYUCh. 9.4 - Prob. 17AYUCh. 9.4 - Prob. 18AYUCh. 9.4 - Prob. 19AYUCh. 9.4 - Prob. 20AYUCh. 9.4 - Prob. 21AYUCh. 9.4 - Prob. 22AYUCh. 9.4 - Prob. 23AYUCh. 9.4 - Prob. 24AYUCh. 9.4 - Prob. 25AYUCh. 9.4 - Prob. 26AYUCh. 9.4 - Prob. 27AYUCh. 9.5 - 1. What is bootstrapping? Be sure to include a...Ch. 9.5 - 2. If we wish to obtain a 95% confidence interval...Ch. 9.5 - Prob. 3AYUCh. 9.5 - Prob. 4AYUCh. 9.5 - Prob. 5AYUCh. 9.5 - Prob. 6AYUCh. 9.5 - Prob. 7AYUCh. 9.5 - Prob. 8AYUCh. 9.5 - Prob. 9AYUCh. 9.5 - 10. Crawling Babies The following data represent...Ch. 9.5 - Prob. 11AYUCh. 9.5 - Prob. 12AYUCh. 9.5 - 13. Bootstrap Proportions To estimate proportions...Ch. 9.5 - 14. Bootstrap Proportions To estimate proportions...Ch. 9.5 - Prob. 15AYUCh. 9.5 - Prob. 16AYUCh. 9.5 - Prob. 17AYUCh. 9.5 - Prob. 18AYUCh. 9.5 - Prob. 19AYUCh. 9.5 - Prob. 20AYUCh. 9.5 - 21. Simulation: What about the Median? Certain...Ch. 9 - Prob. 1RECh. 9 - Prob. 2RECh. 9 - Prob. 3RECh. 9 - Prob. 4RECh. 9 - Prob. 5RECh. 9 - Prob. 6RECh. 9 - Prob. 7RECh. 9 - Prob. 8RECh. 9 - Prob. 9RECh. 9 - Prob. 10RECh. 9 - Prob. 11RECh. 9 - Prob. 12RECh. 9 - Prob. 13RECh. 9 - Prob. 14RECh. 9 - Prob. 15RECh. 9 - Prob. 16RECh. 9 - Prob. 17RECh. 9 - Prob. 1CTCh. 9 - 2. Find the critical values and required to...Ch. 9 - Prob. 3CTCh. 9 - Prob. 4CTCh. 9 - Prob. 5CTCh. 9 - Prob. 6CTCh. 9 - Prob. 7CTCh. 9 - 8. Wimbledon Match Lengths A tennis enthusiast...Ch. 9 - Prob. 9CTCh. 9 - Prob. CS
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