Statistics: Informed Decisions Using Data, Books a la Carte Edition plus NEW MyLab Statistics with Pearson eText-- Access Card Package (5th Edition)
5th Edition
ISBN: 9780134136783
Author: Michael Sullivan III
Publisher: PEARSON
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Chapter 6.2, Problem 17AYU
To determine
The binomial probability for x
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Question 1. Your manager asks you to explain why the Black-Scholes model may be inappro-
priate for pricing options in practice. Give one reason that would substantiate this claim?
Question 2. We consider stock #1 and stock #2 in the model of Problem 2. Your manager
asks you to pick only one of them to invest in based on the model provided. Which one do you
choose and why ?
Question 3. Let (St) to be an asset modeled by the Black-Scholes SDE. Let Ft be the price
at time t of a European put with maturity T and strike price K. Then, the discounted option
price process (ert Ft) t20 is a martingale. True or False? (Explain your answer.)
Question 4. You are considering pricing an American put option using a Black-Scholes model
for the underlying stock. An explicit formula for the price doesn't exist. In just a few words (no
more than 2 sentences), explain how you would proceed to price it.
Question 5. We model a short rate with a Ho-Lee model drt = ln(1+t) dt +2dWt. Then the
interest rate…
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.)
The managing director of a consulting group has the accompanying monthly data on total overhead costs and professional labor hours to bill to clients. Complete parts a through c.
Question content area bottom
Part 1
a. Develop a simple linear regression model between billable hours and overhead costs.
Overhead
Costsequals=212495.2212495.2plus+left parenthesis 42.4857 right parenthesis42.485742.4857times×Billable
Hours
(Round the constant to one decimal place as needed. Round the coefficient to four decimal places as needed. Do not include the $ symbol in your answers.)
Part 2
b. Interpret the coefficients of your regression model. Specifically, what does the fixed component of the model mean to the consulting firm?
Interpret the fixed term,
b 0b0,
if appropriate. Choose the correct answer below.
A.
The value of
b 0b0
is the predicted billable hours for an overhead cost of 0 dollars.
B.
It is not appropriate to interpret
b 0b0,
because its value…
Chapter 6 Solutions
Statistics: Informed Decisions Using Data, Books a la Carte Edition plus NEW MyLab Statistics with Pearson eText-- Access Card Package (5th Edition)
Ch. 6.1 - 1. What is a random variable?
Ch. 6.1 - 2. What is the difference between a discrete...Ch. 6.1 - Prob. 3AYUCh. 6.1 - Prob. 4AYUCh. 6.1 - In Problems 5–8, determine whether the random...Ch. 6.1 - In Problems 5–8, determine whether the random...Ch. 6.1 - In Problems 5–8, determine whether the random...Ch. 6.1 - In Problems 5–8, determine whether the random...Ch. 6.1 - In Problems 9–14, determine whether the...Ch. 6.1 - In Problems 9–14, determine whether the...
Ch. 6.1 - In Problems 9–14, determine whether the...Ch. 6.1 - In Problems 9–14, determine whether the...Ch. 6.1 - In Problems 9–14, determine whether the...Ch. 6.1 - In Problems 9–14, determine whether the...Ch. 6.1 - In Problems 15 and 16, determine the required...Ch. 6.1 - In Problems 15 and 16, determine the required...Ch. 6.1 - NW 17. Televisions In the Sullivan Statistics...Ch. 6.1 - 18. Marriage In the following probability...Ch. 6.1 - 19. Ichiro's Hit Parade In the 2004 baseball...Ch. 6.1 - 20. Waiting in Line A Wendy's manager performed a...Ch. 6.1 - In Problems 21 and 22, (a) construct a discrete...Ch. 6.1 - In Problems 21 and 22, (a) construct a discrete...Ch. 6.1 - 23. Number of Births The graph of the discrete...Ch. 6.1 - 24. Rental Units The graph of the discrete...Ch. 6.1 - 25. Life Insurance A life insurance company sells...Ch. 6.1 - 26. Life Insurance A life insurance company sells...Ch. 6.1 - 27. BlackJack BlackJack is a popular casino game...Ch. 6.1 - 28. Investment An investment counselor calls with...Ch. 6.1 - 29. Roulette In the game of roulette, a player can...Ch. 6.1 - 30. Connecticut Lottery In the Cash Five Lottery...Ch. 6.1 - 31. Powerball Powerball is a multistate lottery....Ch. 6.1 - 32. SAT Test Penalty Some standardized tests, such...Ch. 6.1 - Prob. 33AYUCh. 6.1 - Prob. 34AYUCh. 6.1 - Prob. 35AYUCh. 6.1 - 36. 2014 Senate Election In the 2014 election,...Ch. 6.2 - 1. A binomial experiment is performed a fixed...Ch. 6.2 - 2. For each trial of a binomial experiment, there...Ch. 6.2 - 3. True or False: In the binomial probability...Ch. 6.2 - 4. The phrase “no more than” is represented by the...Ch. 6.2 - 5. The expected number of successes in a binomial...Ch. 6.2 - 6. As a rule of thumb, if ______, the probability...Ch. 6.2 - In Problems 7–16, determine which of the following...Ch. 6.2 - In Problems 7–16, determine which of the following...Ch. 6.2 - In Problems 7–16, determine which of the following...Ch. 6.2 - In Problems 7–16, determine which of the following...Ch. 6.2 - In Problems 7–16, determine which of the following...Ch. 6.2 - In Problems 7–16, determine which of the following...Ch. 6.2 - In Problems 7–16, determine which of the following...Ch. 6.2 - In Problems 7–16, determine which of the following...Ch. 6.2 - In Problems 7–16, determine which of the following...Ch. 6.2 - Prob. 16AYUCh. 6.2 - In Problems 17–28, a binomial probability...Ch. 6.2 - In Problems 17–28, a binomial probability...Ch. 6.2 - In Problems 17–28, a binomial probability...Ch. 6.2 - In Problems 17–28, a binomial probability...Ch. 6.2 - In Problems 17–28, a binomial probability...Ch. 6.2 - Prob. 22AYUCh. 6.2 - In Problems 17–28, a binomial probability...Ch. 6.2 - Prob. 24AYUCh. 6.2 - In Problems 17–28, a binomial probability...Ch. 6.2 - In Problems 17–28, a binomial probability...Ch. 6.2 - In Problems 17–28, a binomial probability...Ch. 6.2 - Prob. 28AYUCh. 6.2 - In Problems 29–34, (a) construct a binomial...Ch. 6.2 - In Problems 29–34, (a) construct a binomial...Ch. 6.2 - In Problems 29–34, (a) construct a binomial...Ch. 6.2 - In Problems 29–34, (a) construct a binomial...Ch. 6.2 - In Problems 29–34, (a) construct a binomial...Ch. 6.2 - In Problems 29–34, (a) construct a binomial...Ch. 6.2 - 35. On-Time Flights According to flightstats.com,...Ch. 6.2 - 36. Morality In a recent poll, the Gallup...Ch. 6.2 - 37. Toilet Flushing In the Healthy Handwashing...Ch. 6.2 - 38. Allergy Sufferers Clarinex-D is a medication...Ch. 6.2 - 39. Sneeze According to a study done by Nick...Ch. 6.2 - 40. Sneeze Revisited According to a study done by...Ch. 6.2 - 41. Jury Selection Twelve jurors are randomly...Ch. 6.2 - 42. Sullivan Survey: Car Color According to paint...Ch. 6.2 - 43. On-Time Flights According to flightstats.com,...Ch. 6.2 - 44. Morality In a recent poll, the Gallup...Ch. 6.2 - 45. Toilet Flushing In the Healthy Handwashing...Ch. 6.2 - Prob. 46AYUCh. 6.2 - Prob. 47AYUCh. 6.2 - Prob. 48AYUCh. 6.2 - Prob. 49AYUCh. 6.2 - Prob. 50AYUCh. 6.2 - 51. Overbooking Flights Historically, the...Ch. 6.2 - Prob. 52AYUCh. 6.2 - Prob. 53AYUCh. 6.2 - Prob. 54AYUCh. 6.2 - Prob. 55AYUCh. 6.2 - Prob. 56AYUCh. 6.2 - Prob. 57AYUCh. 6.2 - Prob. 58AYUCh. 6.2 - Prob. 59AYUCh. 6.2 - 60. When can the Empirical Rule be used to...Ch. 6.3 - Prob. 1AYUCh. 6.3 - 2. Explain the role of λ and t in the Poisson...Ch. 6.3 - In Problems 3–6, state the values of λ and t for...Ch. 6.3 - In Problems 3–6, state the values of λ and t for...Ch. 6.3 - In Problems 3–6, state the values of λ and t for...Ch. 6.3 - In Problems 3–6, state the values of λ and t for...Ch. 6.3 - In Problems 7 and 8, the random variable X follows...Ch. 6.3 - Prob. 8AYUCh. 6.3 - Prob. 9AYUCh. 6.3 - Prob. 10AYUCh. 6.3 - 11. Hits to a Website The number of hits to a...Ch. 6.3 - Prob. 12AYUCh. 6.3 - Prob. 13AYUCh. 6.3 - 14. Potholes The potholes on a major highway in...Ch. 6.3 - Prob. 15AYUCh. 6.3 - 16. Traffic Fatalities According to...Ch. 6.3 - 17. Florida Hurricanes From 1900 to 2014 (115...Ch. 6.3 - Prob. 18AYUCh. 6.3 - Prob. 19AYUCh. 6.3 - Prob. 20AYUCh. 6.3 - Prob. 21AYUCh. 6.3 - Prob. 22AYUCh. 6.3 - 23. Simulation According to the National Center...Ch. 6.3 - Prob. 24AYUCh. 6 - Prob. 1RECh. 6 - Prob. 2RECh. 6 - Prob. 3RECh. 6 - Prob. 4RECh. 6 - Prob. 5RECh. 6 - 6. Emergency Room Visits The probability that a...Ch. 6 - 7. Driving Age According to a Gallup poll, 60% of...Ch. 6 - Prob. 8RECh. 6 - 9. State the condition required to use the...Ch. 6 - Prob. 10RECh. 6 - Prob. 11RECh. 6 - Prob. 12RECh. 6 - Prob. 13RECh. 6 - Prob. 14RECh. 6 - Prob. 15RECh. 6 - Prob. 1CTCh. 6 - Prob. 2CTCh. 6 - Prob. 3CTCh. 6 - Prob. 4CTCh. 6 - Prob. 5CTCh. 6 - Prob. 6CTCh. 6 - Prob. 7CTCh. 6 - Prob. 8CTCh. 6 - Prob. 9CTCh. 6 - Prob. 10CTCh. 6 - Prob. 11CTCh. 6 - Prob. 1CSCh. 6 - 2. Does it appear that, on average, the Neuländers...Ch. 6 - Prob. 3CSCh. 6 - Prob. 4CSCh. 6 - Prob. 5CSCh. 6 - Prob. 6CS
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- Using the accompanying Home Market Value data and associated regression line, Market ValueMarket Valueequals=$28,416+$37.066×Square Feet, compute the errors associated with each observation using the formula e Subscript ieiequals=Upper Y Subscript iYiminus−ModifyingAbove Upper Y with caret Subscript iYi and construct a frequency distribution and histogram. LOADING... Click the icon to view the Home Market Value data. Question content area bottom Part 1 Construct a frequency distribution of the errors, e Subscript iei. (Type whole numbers.) Error Frequency minus−15 comma 00015,000less than< e Subscript iei less than or equals≤minus−10 comma 00010,000 0 minus−10 comma 00010,000less than< e Subscript iei less than or equals≤minus−50005000 5 minus−50005000less than< e Subscript iei less than or equals≤0 21 0less than< e Subscript iei less than or equals≤50005000 9…arrow_forwardThe managing director of a consulting group has the accompanying monthly data on total overhead costs and professional labor hours to bill to clients. Complete parts a through c Overhead Costs Billable Hours345000 3000385000 4000410000 5000462000 6000530000 7000545000 8000arrow_forwardUsing the accompanying Home Market Value data and associated regression line, Market ValueMarket Valueequals=$28,416plus+$37.066×Square Feet, compute the errors associated with each observation using the formula e Subscript ieiequals=Upper Y Subscript iYiminus−ModifyingAbove Upper Y with caret Subscript iYi and construct a frequency distribution and histogram. Square Feet Market Value1813 911001916 1043001842 934001814 909001836 1020002030 1085001731 877001852 960001793 893001665 884001852 1009001619 967001690 876002370 1139002373 1131001666 875002122 1161001619 946001729 863001667 871001522 833001484 798001589 814001600 871001484 825001483 787001522 877001703 942001485 820001468 881001519 882001518 885001483 765001522 844001668 909001587 810001782 912001483 812001519 1007001522 872001684 966001581 86200arrow_forward
- For a binary asymmetric channel with Py|X(0|1) = 0.1 and Py|X(1|0) = 0.2; PX(0) = 0.4 isthe probability of a bit of “0” being transmitted. X is the transmitted digit, and Y is the received digit.a. Find the values of Py(0) and Py(1).b. What is the probability that only 0s will be received for a sequence of 10 digits transmitted?c. What is the probability that 8 1s and 2 0s will be received for the same sequence of 10 digits?d. What is the probability that at least 5 0s will be received for the same sequence of 10 digits?arrow_forwardV2 360 Step down + I₁ = I2 10KVA 120V 10KVA 1₂ = 360-120 or 2nd Ratio's V₂ m 120 Ratio= 360 √2 H I2 I, + I2 120arrow_forwardQ2. [20 points] An amplitude X of a Gaussian signal x(t) has a mean value of 2 and an RMS value of √(10), i.e. square root of 10. Determine the PDF of x(t).arrow_forward
- 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.arrow_forwardProblem 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…arrow_forwardProblem 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…arrow_forward
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