Statistics for Business and Economics (13th Edition)
13th Edition
ISBN: 9780134506593
Author: James T. McClave, P. George Benson, Terry Sincich
Publisher: PEARSON
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Textbook Question
Chapter 4.2, Problem 4.1AE
Use the apple! Random Numbers to generate a list of 25 numbers between 1 and 3, inclusive. Let x represent a number chosen from this list.
- a. What are the possible values of x?
- b. Write a
probability distribution for x in table form. - c. Use the probability distribution in part b to find the expected value of x.
- d. Let y be a number randomly chosen from the set {1, 2, 3}. Write a probability distribution for y in table form and use it to find the expected value of y.
- e. Compare the
expected values of x and yin parts c and d. Why should these two numbers be approximately the same?
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Students have asked these similar questions
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…
The scores of 8 students on the midterm exam and final exam were as follows.
Student
Midterm
Final
Anderson
98
89
Bailey
88
74
Cruz
87
97
DeSana
85
79
Erickson
85
94
Francis
83
71
Gray
74
98
Harris
70
91
Find the value of the (Spearman's) rank correlation coefficient test statistic that would be used to test the claim of no correlation between midterm score and final exam score. Round your answer to 3 places after the decimal point, if necessary.
Test statistic: rs =
Chapter 4 Solutions
Statistics for Business and Economics (13th Edition)
Ch. 4.1 - Types of random variables. Which of the following...Ch. 4.1 - Types of finance random variables. Security...Ch. 4.1 - NHTSA crash tests. Refer to the National Highway...Ch. 4.1 - Customers in line at a Subway shop. The number of...Ch. 4.1 - Executive pay. Refer to Glassdoor Economic...Ch. 4.1 - Banking. Give an example of a discrete random...Ch. 4.1 - Economics. Give an example of a continuous random...Ch. 4.1 - Hotel management. Give an example of a discrete...Ch. 4.1 - Retailing. Give two examples of discrete random...Ch. 4.1 - Stock market. Give an example of a continuous...
Ch. 4.2 - A discrete random variable x can assume five...Ch. 4.2 - The random variable x has the following discrete...Ch. 4.2 - A discrete random variable x can assume five...Ch. 4.2 - Explain why each of the following is or is not a...Ch. 4.2 - A die is tossed. Let x be the number of spots...Ch. 4.2 - Toss three fair coins and let x equal the number...Ch. 4.2 - Use the apple! Random Numbers to generate a list...Ch. 4.2 - Run the applet Simulating the Probability of a...Ch. 4.2 - Consider the probability distribution shown here:...Ch. 4.2 - Consider the probability distribution for the...Ch. 4.2 - Consider the probability distributions shown here:...Ch. 4.2 - Apps not working on smartphone. In a Pew Research...Ch. 4.2 - NHTSA crash tests. Refer to the NHTSA crash tests...Ch. 4.2 - Ages of dot-com employees. The age (in years)...Ch. 4.2 - Variable speed limit control for freeways. A...Ch. 4.2 - Choosing portable grill displays. Refer to the...Ch. 4.2 - Do social robots walk or roll? Refer to the...Ch. 4.2 - Reliability of a manufacturing network. A team of...Ch. 4.2 - Prob. 4.27ACICh. 4.2 - Prob. 4.28ACICh. 4.2 - Contaminated gun cartridges. A weapons...Ch. 4.2 - The last name effect in purchasing. The Journal of...Ch. 4.2 - Mail rooms contaminated with anthrax. During...Ch. 4.2 - Investment risk analysis. The risk of a portfolio...Ch. 4.2 - Prob. 4.33ACICh. 4.2 - Stock market participation and IQ. Refer to The...Ch. 4.2 - Expected loss due to flood damage. The National...Ch. 4.2 - Expected Lotto winnings. Most states offer weekly...Ch. 4.2 - Prob. 4.37ACACh. 4.2 - Prob. 4.38ACACh. 4.2 - Prob. 4.39ACACh. 4.3 - Compute the following: a. 6!2!(62)! b. (52) c....Ch. 4.3 - Consider the following probability distribution:...Ch. 4.3 - Suppose x is a binomial random variable with n = 3...Ch. 4.3 - If x is a binomial random variable, compute p (x)...Ch. 4.3 - If x is a binomial random variable, use Table I in...Ch. 4.3 - If x is a binomial random variable, calculate , 2,...Ch. 4.3 - The binomial probability distribution is a family...Ch. 4.3 - Use the applets Simulating the Probability of a...Ch. 4.3 - Open the applet Sample from a Population. On the...Ch. 4.3 - Use the applet Simulating the Stock Market to...Ch. 4.3 - Working on summer vacation. Recall (Exercise 3.13,...Ch. 4.3 - Privacy and information sharing. Some grocery...Ch. 4.3 - Hotel guest satisfaction. Each year, J. D. Power...Ch. 4.3 - Physicians opinions on a career in medicine. The...Ch. 4.3 - Playing sports related to job pay. Does...Ch. 4.3 - Immediate feedback to incorrect exam answers....Ch. 4.3 - Fingerprint expertise. Refer to the Psychological...Ch. 4.3 - Making your vote count. Refer to the Chance (Fall...Ch. 4.3 - Bridge inspection ratings. According to the...Ch. 4.3 - Tax returns audited by the IRS. According to the...Ch. 4.3 - FDA report on pesticides in food. Periodically,...Ch. 4.3 - Prob. 4.58ACACh. 4.3 - USGA golf ball specifications. According to the...Ch. 4.3 - Network forensic analysis. A network forensic...Ch. 4.4 - Consider the probability distribution shown here:...Ch. 4.4 - Assume that x is a random variable having a...Ch. 4.4 - Prob. 4.63LMCh. 4.4 - Prob. 4.64LMCh. 4.4 - Prob. 4.65LMCh. 4.4 - Suppose x is a random variable for which a Poisson...Ch. 4.4 - Prob. 4.67LMCh. 4.4 - Prob. 4.68LMCh. 4.4 - Prob. 4.69ACBCh. 4.4 - FDIC bank failures. The Federal Deposit Insurance...Ch. 4.4 - Airline fatalities. Over the past 5 years, U.S....Ch. 4.4 - Male nannies. According to the International Nanny...Ch. 4.4 - Contaminated gun cartridges. Refer to the...Ch. 4.4 - Prob. 4.74ACBCh. 4.4 - Prob. 4.75ACICh. 4.4 - Traffic fatalities and sporting events. The...Ch. 4.4 - Prob. 4.77ACICh. 4.4 - Guilt in decision making. The Journal of...Ch. 4.4 - Flaws in plastic-coated wire. The British Columbia...Ch. 4.4 - Making high-stakes insurance decisions. The...Ch. 4.4 - Prob. 4.81ACACh. 4.4 - Waiting for a car wash. An automatic car wash...Ch. 4.4 - Elevator passenger arrivals. A study of the...Ch. 4.6 - Find the area under the standard normal...Ch. 4.6 - Find the following probabilities for the standard...Ch. 4.6 - Find the following probabilities for the standard...Ch. 4.6 - Find each of the following probabilities for the...Ch. 4.6 - Find a value of the standard normal random...Ch. 4.6 - Find a value of the standard normal random...Ch. 4.6 - Give the z-score for a measurement from a normal...Ch. 4.6 - Suppose the random variable x is best described by...Ch. 4.6 - The random variable x has a normal distribution...Ch. 4.6 - Suppose x is a normally distributed random...Ch. 4.6 - Suppose x is a normally distributed random...Ch. 4.6 - Suppose x is a binomial random variable with p =...Ch. 4.6 - Assume that x is a binomial random variable with n...Ch. 4.6 - Open the applet Sample from a Population. On the...Ch. 4.6 - Variable life insurance return rates. With a...Ch. 4.6 - Hotels use of ecolabels. Refer to the Journal of...Ch. 4.6 - Tomato as a taste modifier. Miraculina protein...Ch. 4.6 - Corporate sustainability of CPA firms. Refer to...Ch. 4.6 - Shopping vehicle and judgment. Refer to the...Ch. 4.6 - Buy-side vs. sell-side analysts earnings...Ch. 4.6 - Blood diamonds. According to Global Research News...Ch. 4.6 - Prob. 4.104ACBCh. 4.6 - Executive networking and firm performance. Refer...Ch. 4.6 - Voltage sags and swells. Refer to the Electrical...Ch. 4.6 - Prob. 4.107ACICh. 4.6 - Safety of underground tunnels. Research published...Ch. 4.6 - Prob. 4.109ACICh. 4.6 - Manufacturing hourly pay rate. Government data...Ch. 4.6 - Personnel dexterity tests. Personnel tests are...Ch. 4.6 - Californias electoral college votes. During a...Ch. 4.6 - Prob. 4.113ACICh. 4.6 - Industrial filling process. The characteristics of...Ch. 4.6 - Prob. 4.115ACACh. 4.6 - Box plots and the standard normal distribution....Ch. 4.7 - If a population data set is normally distributed,...Ch. 4.7 - Prob. 4.118LMCh. 4.7 - Prob. 4.119LMCh. 4.7 - Examine the sample data in the accompanying table....Ch. 4.7 - Prob. 4.121ACBCh. 4.7 - Prob. 4.122ACBCh. 4.7 - Drug content assessment. Scientists at...Ch. 4.7 - Prob. 4.124ACBCh. 4.7 - Prob. 4.125ACBCh. 4.7 - Wear-out of used display panels. Wear-out failure...Ch. 4.7 - Rankings of research universities. Refer to the...Ch. 4.7 - Sanitation inspection of cruise ships. Refer to...Ch. 4.7 - Ranking driving performance of professional...Ch. 4.7 - Permeability of sandstone during weathering. Refer...Ch. 4.7 - Prob. 4.131ACACh. 4.8 - Suppose x is a random variable best described by a...Ch. 4.8 - Suppose x is a random variable best described by a...Ch. 4.8 - Refer to Exercise 4.133. Find the following...Ch. 4.8 - Suppose x has an exponential distribution with =...Ch. 4.8 - Prob. 4.136LMCh. 4.8 - Prob. 4.137LMCh. 4.8 - Prob. 4.138LMCh. 4.8 - Prob. 4.7AECh. 4.8 - Prob. 4.8AECh. 4.8 - Load on timber beams. Timber beams are widely used...Ch. 4.8 - Preventative maintenance tests. The optimal...Ch. 4.8 - Maintaining pipe wall temperature. Maintaining a...Ch. 4.8 - Detecting anthrax. Researchers at the University...Ch. 4.8 - Lead in metal shredder residue. On the basis of...Ch. 4.8 - Critical-part failures in NASCAR vehicles. In...Ch. 4.8 - Social network densities. Social networking sites...Ch. 4.8 - Boeing 787 Dreamliner. An assessment of the new...Ch. 4.8 - Soft-drink dispenser. The manager of a local...Ch. 4.8 - Prob. 4.148ACICh. 4.8 - Prob. 4.149ACICh. 4.8 - Cycle availability of a system. In the jargon of...Ch. 4.8 - Prob. 4.151ACICh. 4.8 - Reliability of CO-ROMs. In Reliability Ques (March...Ch. 4.8 - Prob. 4.153ACACh. 4.8 - Reliability of a robotic device. The reliability...Ch. 4.8 - Prob. 4.155ACACh. 4 - For each of the following examples, decide whether...Ch. 4 - Given that x is a binomial random variable,...Ch. 4 - Consider the discrete probability distribution...Ch. 4 - Suppose x is a binomial random variable with n =...Ch. 4 - Suppose x is a Poisson random variable. Compute p...Ch. 4 - Identify the type of random variablebinomial,...Ch. 4 - Prob. 4.162LMCh. 4 - Which of the following describe discrete random...Ch. 4 - Assume that x is a random variable best described...Ch. 4 - Find the following probabilities for the standard...Ch. 4 - Find a z-score, call it z0, such that a. P (z z0)...Ch. 4 - Identify the type of continuous random...Ch. 4 - Assume that x has an exponential distribution with...Ch. 4 - The random variable x has a normal distribution...Ch. 4 - Assume that x is a binomial random variable with n...Ch. 4 - The random variable x has a normal distribution...Ch. 4 - Analysis of bottled water. Is the bottled water...Ch. 4 - Downloading apps to your cell phone. According to...Ch. 4 - LASIK surgery complications. According to studies,...Ch. 4 - Requests to a Web server. According to Brighton...Ch. 4 - NASA and rare planet transits. A planet transit is...Ch. 4 - Hospital patient interarrival times. The length of...Ch. 4 - Dutch elm disease. A nursery advertises that it...Ch. 4 - Tracking missiles with satellite imagery. The...Ch. 4 - The business of casino gaming. Casino gaming...Ch. 4 - Machine repair times. An article in IEEE...Ch. 4 - Public transit deaths. Millions of suburban...Ch. 4 - On-site treatment of hazardous waste. The Resource...Ch. 4 - When to replace a maintenance system. An article...Ch. 4 - Software file updates. Software configuration...Ch. 4 - NHTSA crash safety tests. Refer to Exercise 4.21...Ch. 4 - Errors in measuring truck weights. To help highway...Ch. 4 - Detecting a computer virus attack. Chance (Winter...Ch. 4 - Whistle-blowing among federal employees....Ch. 4 - Ambulance response time. Ambulance response time...Ch. 4 - Optimal goal target in soccer. When attempting to...Ch. 4 - Marine losses for an oil company. The frequency...Ch. 4 - Reliability of a flow network. The journal...Ch. 4 - Doctors and ethics. Refer to the Journal of...Ch. 4 - Prob. 4.195ACICh. 4 - Testing for spoiled wine. Suppose that you are...Ch. 4 - Estimating demand for white bread. A bakery has...Ch. 4 - Checkout lanes at a supermarket. A team of...Ch. 4 - Rating employee performance. Almost all companies...Ch. 4 - Ship-to-shore transfer times. Lack of port...Ch. 4 - Prob. 4.201ACACh. 4 - Establishing tolerance limits. The tolerance...Ch. 4 - The showcase showdown. On the popular television...Ch. 4 - Reliability of a one-shot device. A one-shot...Ch. 4 - Super weapons development. The U.S. Army is...Ch. 4 - Space shuttle disaster. On January 28, 1986, the...Ch. 4 - Warehouse clubs are retailers that offer lower...Ch. 4 - Prob. 4.1.2ACh. 4 - Prob. 4.1.3ACh. 4 - Prob. 4.1.4ACh. 4 - Prob. 4.1.5ACh. 4 - Prob. 4.1.6ACh. 4 - Prob. 4.1.7ACh. 4 - Warehouse clubs are retailers that offer lower...
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