INTRODUCTION TO STATISTICS & DATA ANALYS
6th Edition
ISBN: 9780357420447
Author: PECK
Publisher: CENGAGE L
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Textbook Question
Chapter 6, Problem 104CR
Use the information given in exercise 6.102 to determine the following
- a. P(E and C and L)
- b. P(E and L)
- c. P(C and L)
- d. P(C|E and L)
6.102 Consider the following information about passengers on a cruise ship on vacation: 40% check work e-mail, 30% use a cell phone to stay connected to work, 25% bring a laptop with them on vacation, 23% both check work e-mail and use a cell phone to stay connected, and 51% neither check work e-mail nor use a cell phone to stay connected nor bring a laptop. In addition, 88% of those who bring a laptop also check work e-mail and 70% of those who use a cell phone to stay connected also bring a laptop. With
E =
C = event that a traveler on vacation uses a cell phone to stay connected
L = event that a traveler on vacation brought a laptop
use the given information to determine the following probabilities. A Venn diagram may help.
- a. P(E)
- b. P(C)
- c. P(L)
- d. P(E and C)
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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.)
Chapter 6 Solutions
INTRODUCTION TO STATISTICS & DATA ANALYS
Ch. 6.1 - Define the term chance experiment, and give an...Ch. 6.1 - Define the term sample space, and then give the...Ch. 6.1 - Consider the chance experiment in which the type...Ch. 6.1 - Refer to the chance experiment described in the...Ch. 6.1 - A tennis shop sells five different brands of...Ch. 6.1 - Refer to the chance experiment described in the...Ch. 6.1 - A new model of laptop computer can be ordered with...Ch. 6.1 - A college library has four copies of a certain...Ch. 6.1 - A library has five copies of a certain textbook on...Ch. 6.1 - Suppose that, starting at a certain time,...
Ch. 6.1 - Refer to the previous exercise and now suppose...Ch. 6.1 - A family consisting of three peopleP1, P2, and...Ch. 6.1 - Prob. 13ECh. 6.1 - An engineering construction firm is currently...Ch. 6.1 - For the events described in the previous exercise,...Ch. 6.1 - Consider a Venn diagram picturing two events A and...Ch. 6.3 - A large department store offers online ordering....Ch. 6.3 - Consider the chance experiment described in the...Ch. 6.3 - The manager of an online music store has kept...Ch. 6.3 - Consider the chance experiment described in the...Ch. 6.3 - A bookstore sells two types of books (fiction and...Ch. 6.3 - Consider the chance experiment described in the...Ch. 6.3 - Medical insurance statuscovered (C) or not covered...Ch. 6.3 - Roulette is a game of chance that involves...Ch. 6.3 - Phoenix is a hub for a large airline. Suppose that...Ch. 6.3 - A customer satisfaction survey is planned. The...Ch. 6.3 - A professor assigns five problems to be completed...Ch. 6.3 - Refer to the following information on full-term...Ch. 6.3 - The report Teens, Social Media Technology...Ch. 6.3 - According to The Chronicle for Higher Education...Ch. 6.3 - The same issue of The Chronicle for Higher...Ch. 6.3 - A deck of 52 playing cards is mixed well, and 5...Ch. 6.3 - After all students have left the classroom, a...Ch. 6.3 - Use the information given in the previous exercise...Ch. 6.3 - The student council for a school of science and...Ch. 6.3 - A student placement center has requests from five...Ch. 6.3 - Suppose that a six-sided die is weighted so that...Ch. 6.4 - Two different airlines have a flight from Los...Ch. 6.4 - The article Chances Are You Know Someone with a...Ch. 6.4 - The accompanying data are from the article...Ch. 6.4 - Using the probabilities calculated in the previous...Ch. 6.4 - The following graphical display is similar to one...Ch. 6.4 - The article Americans Growing More Concerned About...Ch. 6.4 - The events E and T are defined as E = the event...Ch. 6.4 - The newspaper article Folic Acid Might Reduce Risk...Ch. 6.4 - Suppose that an individual is randomly selected...Ch. 6.4 - Is ultrasound a reliable method for determining...Ch. 6.4 - The paper Accuracy and Reliability of...Ch. 6.4 - The report 2015 Utah Seat Belt Use Survey (Utah...Ch. 6.4 - The National Highway Traffic Safety Administration...Ch. 6.4 - Use the information given in the previous exercise...Ch. 6.4 - The paper Good for Women, Good for Men, Bad for...Ch. 6.5 - Many fire stations handle emergency calls for...Ch. 6.5 - Refer to the information given in the previous...Ch. 6.5 - The paper Predictors of Complementary Therapy Use...Ch. 6.5 - The report TV Drama/Comedy Viewers and Health...Ch. 6.5 - The report Great Jobs, Great Lives. The...Ch. 6.5 - In a small city, approximately 15% of those...Ch. 6.5 - Jeanie is a bit forgetful, and if she doesnt make...Ch. 6.5 - Consider a system consisting of four components,...Ch. 6.5 - Consider the system described in the previous...Ch. 6.5 - In a January 2016 Harris Poll, each of 2252...Ch. 6.5 - Consider the following events: T = event that a...Ch. 6.5 - The following case study was reported in the...Ch. 6.5 - Three friends (A, B, and C) will participate in a...Ch. 6.5 - A store sells two different brands of dishwasher...Ch. 6.5 - The National Public Radio show Car Talk used to...Ch. 6.5 - Refer to the previous exercise. Suppose now that...Ch. 6.6 - A university has 10 vehicles available for use by...Ch. 6.6 - Prob. 70ECh. 6.6 - There are two traffic lights on Darlenes route...Ch. 6.6 - Let F denote the event that a randomly selected...Ch. 6.6 - According to a July 31, 2013 posting on cnn.com, a...Ch. 6.6 - Suppose that Blue Cab operates 15% of the taxis in...Ch. 6.6 - A large cable company reports the following: 80%...Ch. 6.6 - Refer to the information given in the previous...Ch. 6.6 - The authors of the paper Do Physicians Know When...Ch. 6.6 - A study of how people are using online services...Ch. 6.6 - The report Twitter in Higher Education: Usage...Ch. 6.6 - Use the information given in the previous exercise...Ch. 6.6 - Prob. 81ECh. 6.6 - Use the table of estimated probabilities from the...Ch. 6.6 - Suppose that we define the following events: C =...Ch. 6.6 - The article U.S. Investors Split Between Digital...Ch. 6.6 - Prob. 85ECh. 6.6 - The paper referenced in the previous exercise also...Ch. 6.6 - In an article that appears on the web site of the...Ch. 6.7 - The report Airline Quality Rating 2016...Ch. 6.7 - Five hundred first-year students at a state...Ch. 6.7 - Use the information given in the previous exercise...Ch. 6.7 - The table given below describes (approximately)...Ch. 6.7 - On April 1, 2010, the Bureau of the Census in the...Ch. 6.7 - Refer to the information given in the previous...Ch. 6.7 - Refer to the information given in Exercises 6.92...Ch. 6 - False positive results are not uncommon with...Ch. 6 - A company uses three different assembly linesA1,...Ch. 6 - Consider the following information about...Ch. 6 - Use the information given in the previous exercise...Ch. 6 - Use the information given in exercise 6.102 to...Ch. 6 - Prob. 105CRCh. 6 - The following table summarizing data on smoking...Ch. 6 - A study of the impact of seeking a second opinion...Ch. 6 - A company sends 40% of its overnight mail parcels...Ch. 6 - Prob. 109CRCh. 6 - Prob. 110CRCh. 6 - In a school machine shop, 60% of all machine...Ch. 6 - There are five faculty members in a certain...Ch. 6 - The general addition rule for three events states...Ch. 6 - A theater complex is currently showing four...Ch. 6 - Prob. 117CRCh. 6 - Suppose that a box contains 25 light bulbs, of...Ch. 6 - Return to Exercise 6.118, and suppose that 4 bulbs...Ch. 6 - A transmitter is sending a message using a binary...
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