Statistics: Informed Decisions Using Data (5th Edition)
5th Edition
ISBN: 9780134133539
Author: Michael Sullivan III
Publisher: PEARSON
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Chapter 10.2, Problem 26AYU
To determine
To perform: Hypothesis testing of one sample proportion.
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In a network with 12 links, one of the links has failed. The failed link is randomlylocated. An electrical engineer tests the links one by one until the failed link is found.a. What is the probability that the engineer will find the failed link in the first test?b. What is the probability that the engineer will find the failed link in five tests?Note: You should assume that for Part b, the five tests are done consecutively.
Problem 3. Pricing a multi-stock option the Margrabe formula
The purpose of this problem is to price a swap option in a 2-stock model, similarly as
what we did in the example in the lectures. We consider a two-dimensional Brownian
motion given by W₁ = (W(¹), W(2)) on a probability space (Q, F,P). Two stock prices
are modeled by the following equations:
dX
=
dY₁ =
X₁ (rdt+
rdt+0₁dW!)
(²)),
Y₁ (rdt+dW+0zdW!"),
with Xo
xo and Yo =yo. This corresponds to the multi-stock model studied in class,
but with notation (X+, Y₁) instead of (S(1), S(2)). Given the model above, the measure
P is already the risk-neutral measure (Both stocks have rate of return r). We write
σ = 0₁+0%. We consider a swap option, which gives you the right, at time T, to
exchange one share of X for one share of Y. That is, the option has payoff
F=(Yr-XT).
(a) We first assume that r = 0 (for questions (a)-(f)). Write an explicit expression for
the process Xt.
Reminder before proceeding to question (b): Girsanov's theorem…
Problem 1. Multi-stock model
We consider a 2-stock model similar to the one studied in class. Namely, we consider
=
S(1)
S(2)
=
S(¹) exp (σ1B(1) + (M1 - 0/1 )
S(²) exp (02B(2) + (H₂-
M2
where (B(¹) ) +20 and (B(2) ) +≥o are two Brownian motions, with
t≥0
Cov (B(¹), B(2)) = p min{t, s}.
"
The purpose of this problem is to prove that there indeed exists a 2-dimensional Brownian
motion (W+)+20 (W(1), W(2))+20 such that
=
S(1)
S(2)
=
=
S(¹) exp (011W(¹) + (μ₁ - 01/1) t)
롱)
S(²) exp (021W (1) + 022W(2) + (112 - 03/01/12) t).
where σ11, 21, 22 are constants to be determined (as functions of σ1, σ2, p).
Hint: The constants will follow the formulas developed in the lectures.
(a) To show existence of (Ŵ+), first write the expression for both W. (¹) and W (2)
functions of (B(1), B(²)).
as
(b) Using the formulas obtained in (a), show that the process (WA) is actually a 2-
dimensional standard Brownian motion (i.e. show that each component is normal,
with mean 0, variance t, and that their…
Chapter 10 Solutions
Statistics: Informed Decisions Using Data (5th Edition)
Ch. 10.1 - 1. A ___________ is a statement regarding a...Ch. 10.1 - 2. ___________ ___________ is a procedure, based...Ch. 10.1 - 3. The ___________ ________ is a statement of no...Ch. 10.1 - 4. The ___________ ___________ is a statement we...Ch. 10.1 - 5. If we reject the null hypothesis when the...Ch. 10.1 - 6. If we do not reject the null hypothesis when...Ch. 10.1 - 7. The ___________ is the probability of making a...Ch. 10.1 - 8. True or False: Sample evidence can prove a null...Ch. 10.1 - Prob. 9AYUCh. 10.1 - In Problems 9–14, the null and alternative...
Ch. 10.1 - Prob. 11AYUCh. 10.1 - Prob. 12AYUCh. 10.1 - Prob. 13AYUCh. 10.1 - Prob. 14AYUCh. 10.1 - In Problems 15–22, (a) determine the null and...Ch. 10.1 - In Problems 15–22, (a) determine the null and...Ch. 10.1 - In Problems 15–22, (a) determine the null and...Ch. 10.1 - In Problems 15–22, (a) determine the null and...Ch. 10.1 - In Problems 15–22, (a) determine the null and...Ch. 10.1 - In Problems 15–22, (a) determine the null and...Ch. 10.1 - In Problems 15–22, (a) determine the null and...Ch. 10.1 - In Problems 15–22, (a) determine the null and...Ch. 10.1 - Prob. 23AYUCh. 10.1 - Prob. 24AYUCh. 10.1 - Prob. 25AYUCh. 10.1 - Prob. 26AYUCh. 10.1 - Prob. 27AYUCh. 10.1 - Prob. 28AYUCh. 10.1 - Prob. 29AYUCh. 10.1 - Prob. 30AYUCh. 10.1 - Prob. 31AYUCh. 10.1 - Prob. 32AYUCh. 10.1 - In Problems 23–34, state the conclusion based on...Ch. 10.1 - Prob. 34AYUCh. 10.1 - Prob. 35AYUCh. 10.1 - Prob. 36AYUCh. 10.1 - 37. E-Cigs According to the Centers for Disease...Ch. 10.1 - 38. Migraines According to the Centers for Disease...Ch. 10.1 - Prob. 39AYUCh. 10.1 - Prob. 40AYUCh. 10.1 - Prob. 41AYUCh. 10.1 - Prob. 42AYUCh. 10.1 - 43. What happens to the probability of making a...Ch. 10.1 - 44. The following is a quotation from Sir Ronald...Ch. 10.1 - 45. In your own words, explain the difference...Ch. 10.2 - 1. When observed results are unlikely under the...Ch. 10.2 - Prob. 2AYUCh. 10.2 - Prob. 3AYUCh. 10.2 - Prob. 4AYUCh. 10.2 - Prob. 5AYUCh. 10.2 - Prob. 6AYUCh. 10.2 - Prob. 7AYUCh. 10.2 - Prob. 8AYUCh. 10.2 - Prob. 9AYUCh. 10.2 - Prob. 10AYUCh. 10.2 - Prob. 11AYUCh. 10.2 - Prob. 12AYUCh. 10.2 - Prob. 13AYUCh. 10.2 - Prob. 14AYUCh. 10.2 - 15. Cramer Correct Less Than Half the Time? The...Ch. 10.2 - 16. Political Pundits In his book, "The Signal and...Ch. 10.2 - NW 17. Lipitor The drug Lipitor is meant to reduce...Ch. 10.2 - 18. Nexium Nexium is a drug that can be used to...Ch. 10.2 - 19. Fatal Traffic Accidents According to the...Ch. 10.2 - 20. Eating Together In December 2001, 38% of...Ch. 10.2 - NW 21. Taught Enough Math? In 1994, 52% of parents...Ch. 10.2 - 22. Living Alone? In 2000, 58% of females aged 15...Ch. 10.2 - Prob. 23AYUCh. 10.2 - Prob. 24AYUCh. 10.2 - Prob. 25AYUCh. 10.2 - Prob. 26AYUCh. 10.2 - Prob. 27AYUCh. 10.2 - 28. Small-Sample Hypothesis Test In 1997, 4% of...Ch. 10.2 - Prob. 29AYUCh. 10.2 - Prob. 30AYUCh. 10.2 - Prob. 31AYUCh. 10.2 - Prob. 32AYUCh. 10.2 - Prob. 33AYUCh. 10.2 - Prob. 34AYUCh. 10.2 - Prob. 35AYUCh. 10.2 - Prob. 36AYUCh. 10.2 - 37. Simulation: Predicting the Future...Ch. 10.2 - Prob. 38AYUCh. 10.2 - 39. Putting It Together: Naughty or Nice? Yale...Ch. 10.2 - Prob. 40AYUCh. 10.2 - Prob. 41AYUCh. 10.2 - Prob. 42AYUCh. 10.2 - Prob. 43AYUCh. 10.2 - Prob. 44AYUCh. 10.2 - Prob. 45AYUCh. 10.3 - 1. (a) Determine the critical value for a...Ch. 10.3 - Prob. 2AYUCh. 10.3 - Prob. 3AYUCh. 10.3 - 4. To test H0: µ = 40 versus H1: > 40, a simple...Ch. 10.3 - 5. To test H0: μ = 100 versus H1: μ ≠ 100, a...Ch. 10.3 - Prob. 6AYUCh. 10.3 - Prob. 7AYUCh. 10.3 - 8. To test H0: μ = 4.5 versus H1: μ > 4.5, a...Ch. 10.3 - Prob. 9AYUCh. 10.3 - Prob. 10AYUCh. 10.3 - Prob. 11AYUCh. 10.3 - Prob. 12AYUCh. 10.3 - NW 13. Ready for College? The ACT is a college...Ch. 10.3 - 14. SAT Verbal Scores Do students who learned...Ch. 10.3 - 15. Effects of Alcohol on the Brain In a study...Ch. 10.3 - 16. Effects of Plastic Resin Para-nonylphenol is...Ch. 10.3 - 17. Credit Scores A Fair Isaac Corporation (FICO)...Ch. 10.3 - 18. TVaholics According to the American Time Use...Ch. 10.3 - 19. Age of Death-Row Inmates In 2002, the mean age...Ch. 10.3 - 20. Energy Consumption In 2001, the mean household...Ch. 10.3 - Prob. 21AYUCh. 10.3 - Prob. 22AYUCh. 10.3 - Prob. 23AYUCh. 10.3 - Prob. 24AYUCh. 10.3 - Prob. 25AYUCh. 10.3 - Prob. 26AYUCh. 10.3 - Prob. 27AYUCh. 10.3 - Prob. 28AYUCh. 10.3 - Prob. 29AYUCh. 10.3 - Prob. 30AYUCh. 10.3 - 31. Statistical Significance versus Practical...Ch. 10.3 - Prob. 32AYUCh. 10.3 - Prob. 33AYUCh. 10.3 - Prob. 34AYUCh. 10.3 - Prob. 35AYUCh. 10.3 - Prob. 36AYUCh. 10.3 - Prob. 37AYUCh. 10.3 - Prob. 38AYUCh. 10.3 - Prob. 39AYUCh. 10.3 - Prob. 40AYUCh. 10.4 - 1. (a) Determine the critical value for a...Ch. 10.4 - Prob. 2AYUCh. 10.4 - Prob. 3AYUCh. 10.4 - Prob. 4AYUCh. 10.4 - Prob. 5AYUCh. 10.4 - Prob. 6AYUCh. 10.4 - Prob. 7AYUCh. 10.4 - Prob. 8AYUCh. 10.4 - NW 9. Mutual Fund Risk One measure of the risk of...Ch. 10.4 - 10. Filling Machine A machine fills bottles with...Ch. 10.4 - 11. Pump Design The piston diameter of a certain...Ch. 10.4 - 12. Counting Carbs The manufacturer of processed...Ch. 10.4 - Prob. 13AYUCh. 10.4 - Prob. 14AYUCh. 10.4 - Prob. 15AYUCh. 10.4 - Prob. 16AYUCh. 10.4 - Prob. 17AYUCh. 10.4 - Prob. 18AYUCh. 10.5 - 1. A simple random sample of size n = 19 is drawn...Ch. 10.5 - 2. A simple random sample of size n = 200...Ch. 10.5 - Prob. 3AYUCh. 10.5 - Prob. 4AYUCh. 10.5 - Prob. 5AYUCh. 10.5 - Prob. 6AYUCh. 10.5 - Prob. 7AYUCh. 10.5 - 8. A simple random sample of size n = 320 adults...Ch. 10.5 - Prob. 9AYUCh. 10.5 - Prob. 10AYUCh. 10.5 - Prob. 11AYUCh. 10.5 - Prob. 12AYUCh. 10.5 - Prob. 13AYUCh. 10.5 - Prob. 14AYUCh. 10.5 - Prob. 15AYUCh. 10.5 - Prob. 16AYUCh. 10.5 - Prob. 17AYUCh. 10.5 - Prob. 18AYUCh. 10.5 - Prob. 19AYUCh. 10.5 - Prob. 20AYUCh. 10.5 - Prob. 21AYUCh. 10.5 - Prob. 22AYUCh. 10.5 - Prob. 23AYUCh. 10.5 - Prob. 24AYUCh. 10.5 - Prob. 25AYUCh. 10.5 - Prob. 26AYUCh. 10.5 - Prob. 27AYUCh. 10.5 - Prob. 28AYUCh. 10.5 - Prob. 29AYUCh. 10.6 - Prob. 1AYUCh. 10.6 - Prob. 2AYUCh. 10.6 - Prob. 3AYUCh. 10.6 - Prob. 4AYUCh. 10.6 - Prob. 5AYUCh. 10.6 - Prob. 6AYUCh. 10.6 - Prob. 7AYUCh. 10.6 - Prob. 8AYUCh. 10.6 - Prob. 9AYUCh. 10.6 - Prob. 10AYUCh. 10.6 - Prob. 11AYUCh. 10.6 - Prob. 12AYUCh. 10.6 - Prob. 13AYUCh. 10.6 - Prob. 14AYUCh. 10.6 - Prob. 15AYUCh. 10.6 - Prob. 16AYUCh. 10.6 - Prob. 17AYUCh. 10.6 - Prob. 18AYUCh. 10.6 - Prob. 19AYUCh. 10.6 - Prob. 20AYUCh. 10.6 - Prob. 21AYUCh. 10.6 - Prob. 22AYUCh. 10 - Prob. 1RECh. 10 - Prob. 2RECh. 10 - Prob. 3RECh. 10 - Prob. 4RECh. 10 - Prob. 5RECh. 10 - Prob. 6RECh. 10 - Prob. 7RECh. 10 - Prob. 8RECh. 10 - Prob. 9RECh. 10 - Prob. 10RECh. 10 - Prob. 11RECh. 10 - Prob. 12RECh. 10 - Prob. 13RECh. 10 - Prob. 14RECh. 10 - Prob. 15RECh. 10 - Prob. 16RECh. 10 - Prob. 17RECh. 10 - Prob. 18RECh. 10 - Prob. 19RECh. 10 - Prob. 20RECh. 10 - Prob. 21RECh. 10 - Prob. 22RECh. 10 - 23. Explain the difference between "accepting" and...Ch. 10 - Prob. 24RECh. 10 - Prob. 25RECh. 10 - Prob. 26RECh. 10 - Prob. 1CTCh. 10 - Prob. 2CTCh. 10 - Prob. 3CTCh. 10 - Prob. 4CTCh. 10 - Prob. 5CTCh. 10 - Prob. 6CTCh. 10 - Prob. 7CTCh. 10 - Prob. 8CTCh. 10 - Prob. 9CTCh. 10 - Prob. CS
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