Applied Statistics and Probability for Engineers
6th Edition
ISBN: 9781118539712
Author: Douglas C. Montgomery
Publisher: WILEY
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Chapter 5, Problem 107SE
To determine
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Students have asked these similar questions
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 5 Solutions
Applied Statistics and Probability for Engineers
Ch. 5.1 - Prob. 1ECh. 5.1 - Prob. 2ECh. 5.1 - Prob. 3ECh. 5.1 - 5-4. Four electronic printers are selected from a...Ch. 5.1 - 5-5. In the transmission of digital information,...Ch. 5.1 - 5-6. A small-business Web site contains 100 pages...Ch. 5.1 - 5-7. A manufacturing company employs two devices...Ch. 5.1 - 5-8. Suppose that the random variables X, Y, and Z...Ch. 5.1 - 5-9. An engineering statistics class has 40...Ch. 5.1 - 5-10. An article in the Journal of Database...
Ch. 5.1 - 5-11. For the Transaction Processing Performance...Ch. 5.1 - 5-12. In the transmission of digital information,...Ch. 5.1 - Prob. 13ECh. 5.1 - Prob. 14ECh. 5.1 - Prob. 15ECh. 5.1 - Prob. 16ECh. 5.1 - Prob. 17ECh. 5.1 - 5-18. The conditional probability distribution of...Ch. 5.1 - Prob. 19ECh. 5.1 - 5-20. The time between surface finish problems in...Ch. 5.1 - 5-21. A popular clothing manufacturer receives...Ch. 5.1 - 5-22. The blade and the bearings are important...Ch. 5.1 - Prob. 23ECh. 5.1 - Prob. 24ECh. 5.1 - 5-25. Determine the value of c that makes fXYZ (x,...Ch. 5.1 - 5-26. The yield in pounds from a day’s production...Ch. 5.1 - 5-27. The weights of adobe bricks used for...Ch. 5.1 - 5-28. A manufacturer of electroluminescent lamps...Ch. 5.1 - 5-29. The lengths of the minor and major axes are...Ch. 5.1 - 5-30. An article in Health Economics [“Estimation...Ch. 5.1 - 5-31. An article in Clinical Infectious Diseases...Ch. 5.1 - Prob. 32ECh. 5.2 - Prob. 33ECh. 5.2 - Prob. 34ECh. 5.2 - Prob. 35ECh. 5.2 - Prob. 36ECh. 5.2 - Prob. 37ECh. 5.2 - Prob. 38ECh. 5.2 - Prob. 39ECh. 5.2 - Prob. 40ECh. 5.2 - Prob. 41ECh. 5.2 - Prob. 42ECh. 5.2 - Prob. 43ECh. 5.2 - 5-44. Determine the covariance and correlation for...Ch. 5.2 - Prob. 45ECh. 5.2 - Prob. 46ECh. 5.2 - Prob. 47ECh. 5.3 - 5-48. Test results from an electronic circuit...Ch. 5.3 - Prob. 49ECh. 5.3 - Prob. 50ECh. 5.3 - 5-51. Four electronic ovens that were dropped...Ch. 5.3 - Prob. 52ECh. 5.3 - Prob. 53ECh. 5.3 - 5-54. In an acid-base titration, a base or acid is...Ch. 5.3 - Prob. 55ECh. 5.3 - Prob. 56ECh. 5.3 - Prob. 58ECh. 5.3 - 5-59. If X and Y have a bivariate normal...Ch. 5.3 - 5-60. Show that the probability density function...Ch. 5.3 - Prob. 61ECh. 5.4 - Prob. 62ECh. 5.4 - 5-63. X and Y are independent, normal random...Ch. 5.4 - 5-64. Suppose that the random variable X...Ch. 5.4 - 5-65. A plastic casing for a magnetic disk is...Ch. 5.4 - 5-66. Making handcrafted pottery generally takes...Ch. 5.4 - 5-67. In the manufacture of electroluminescent...Ch. 5.4 - 5-68. The width of a casing for a door is normally...Ch. 5.4 - 5-69. An article in Knee Surgery Sports...Ch. 5.4 - 5-70. An automated filling machine fills...Ch. 5.4 - 5-71. The photoresist thickness in semiconductor...Ch. 5.4 - 5-72. Assume that the weights of individuals are...Ch. 5.4 - 5-73. Weights of parts are normally distributed...Ch. 5.4 - Prob. 74ECh. 5.4 - Prob. 75ECh. 5.4 - Prob. 76ECh. 5.4 - Prob. 77ECh. 5.4 - Prob. 78ECh. 5.5 - 5-79. Suppose that X is a random variable with...Ch. 5.5 - 5-80. Let X be a binomial random variable with p =...Ch. 5.5 - 5-81. Suppose that X is a continuous random...Ch. 5.5 - 5-83. A random variable X has the probability...Ch. 5.5 - Prob. 84ECh. 5.5 - Prob. 85ECh. 5.5 - Prob. 86ECh. 5.5 - Prob. 87ECh. 5.5 - Prob. 88ECh. 5.5 - 5-89. The computational time of a statistical...Ch. 5.5 - Prob. 90ECh. 5.6 - Prob. 91ECh. 5.6 - Prob. 92ECh. 5.6 - 5-93. The geometric random variable X has...Ch. 5.6 - 5-94. The chi-squared random variable with k...Ch. 5.6 - Prob. 95ECh. 5.6 - Prob. 96ECh. 5.6 - Prob. 98ECh. 5.6 - Prob. 99ECh. 5.6 - 5-100. Suppose that Xi has a normal distribution...Ch. 5 - Prob. 101SECh. 5 - 5-102. The percentage of people given an...Ch. 5 - Prob. 103SECh. 5 - Prob. 104SECh. 5 - Prob. 105SECh. 5 - Prob. 106SECh. 5 - Prob. 107SECh. 5 - Prob. 108SECh. 5 - Prob. 109SECh. 5 - 5-110. The weight of adobe bricks for construction...Ch. 5 - Prob. 111SECh. 5 - Prob. 112SECh. 5 - Prob. 113SECh. 5 - Prob. 114SECh. 5 - Prob. 116SECh. 5 - Prob. 117SECh. 5 - Prob. 118SECh. 5 - Prob. 119SECh. 5 - 5-120. An order of 15 printers contains 4 with a...Ch. 5 - Prob. 121SECh. 5 - Prob. 122SECh. 5 - Prob. 123SECh. 5 - Prob. 124SECh. 5 - Prob. 125SECh. 5 - Prob. 126SECh. 5 - Prob. 127SECh. 5 - Prob. 128SECh. 5 - Prob. 129SECh. 5 - Prob. 130SECh. 5 - Prob. 131SECh. 5 - Prob. 132SE
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