Statistical Reasoning for Everyday Life (5th Edition)
5th Edition
ISBN: 9780134494043
Author: Jeff Bennett, William L. Briggs, Mario F. Triola
Publisher: PEARSON
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Chapter 5.2, Problem 44E
a.
To determine
Find the percentage of movies that take more than 2 hours long.
b.
To determine
Find the percentage of movies that are less than
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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 5 Solutions
Statistical Reasoning for Everyday Life (5th Edition)
Ch. 5.1 - Normal Distribution. When we refer to a normal...Ch. 5.1 - Normal Shape. Draw a rough sketch of a normal...Ch. 5.1 - Area Under the Curve. What does the area under the...Ch. 5.1 - Normal Conditions. Briefly describe the four...Ch. 5.1 - Does It Make Sense? For Exercises 58, determine...Ch. 5.1 - Does It Make Sense? For Exercises 58, determine...Ch. 5.1 - Does It Make Sense? For Exercises 58, determine...Ch. 5.1 - Does It Make Sense? For Exercises 58, determine...Ch. 5.1 - What Is Normal? Identify the distribution in...Ch. 5.1 - What Is Normal? Identify the distribution in...
Ch. 5.1 - Normal Distributions. For each of the data sets in...Ch. 5.1 - Normal Distributions. For each of the data sets in...Ch. 5.1 - Normal Distributions. For each of the data sets in...Ch. 5.1 - Normal Distributions. For each of the data sets in...Ch. 5.1 - Normal Distributions. For each of the data sets in...Ch. 5.1 - Normal Distributions. For each of the data sets in...Ch. 5.1 - Normal Distributions. For each of the data sets in...Ch. 5.1 - Normal Distributions. For each of the data sets in...Ch. 5.1 - Body Temperature. Figure 5.8 shows a histogram for...Ch. 5.1 - Cotinine. The amount of nicotine absorbed by the...Ch. 5.1 - Departure Delay Times. Figure 5.10 on the next...Ch. 5.1 - MM Weights. Figure 5.11 shows a histogram for the...Ch. 5.1 - Areas and Relative Frequencies. Consider the graph...Ch. 5.1 - Areas and Relative Frequencies. Consider the graph...Ch. 5.1 - Estimating Areas. Consider the graph of the normal...Ch. 5.1 - Prob. 26ECh. 5.2 - The 68-95-99.7 Rule. What is the 68-95-99.7 rule...Ch. 5.2 - Applying the 68-95-99.7 Rule. For a normal...Ch. 5.2 - Standard Score. What is a standard score? How do...Ch. 5.2 - Percentiles. What is a percentile? Describe how...Ch. 5.2 - Does It Make Sense? For Exercises 58, determine...Ch. 5.2 - Does It Make Sense? For Exercises 58, determine...Ch. 5.2 - Does It Make Sense? For Exercises 58, determine...Ch. 5.2 - Does It Make Sense? For Exercises 58, determine...Ch. 5.2 - Using the 68-95-99.7 Rule. A test of depth...Ch. 5.2 - Using the 68-95-99.7 Rule. Pulse rates for adult...Ch. 5.2 - Applying the 68-95-99.7 Rule. In a study of facial...Ch. 5.2 - Applying the 68-95-99.7 Rule. Adult males have...Ch. 5.2 - IQ Scores. For Exercises 1324, sketch the normal...Ch. 5.2 - IQ Scores. For Exercises 1324, sketch the normal...Ch. 5.2 - IQ Scores. For Exercises 1324, sketch the normal...Ch. 5.2 - IQ Scores. For Exercises 1324, sketch the normal...Ch. 5.2 - IQ Scores. For Exercises 1324, sketch the normal...Ch. 5.2 - IQ Scores. For Exercises 1324, sketch the normal...Ch. 5.2 - IQ Scores. For Exercises 1324, sketch the normal...Ch. 5.2 - Prob. 20ECh. 5.2 - Prob. 21ECh. 5.2 - Prob. 22ECh. 5.2 - Prob. 23ECh. 5.2 - IQ Scores. For Exercises 1324, sketch the normal...Ch. 5.2 - Heights of Males. For Exercises 2536, sketch the...Ch. 5.2 - Heights of Males. For Exercises 2536, sketch the...Ch. 5.2 - Heights of Males. For Exercises 2536, sketch the...Ch. 5.2 - Heights of Males. For Exercises 2536, sketch the...Ch. 5.2 - Heights of Males. For Exercises 2536, sketch the...Ch. 5.2 - Heights of Males. For Exercises 2536, sketch the...Ch. 5.2 - Heights of Males. For Exercises 2536, sketch the...Ch. 5.2 - Heights of Males. For Exercises 2536, sketch the...Ch. 5.2 - Heights of Males. For Exercises 2536, sketch the...Ch. 5.2 - Heights of Males. For Exercises 2536, sketch the...Ch. 5.2 - Heights of Males. For Exercises 2536, sketch the...Ch. 5.2 - Heights of Males. For Exercises 2536, sketch the...Ch. 5.2 - Coin Weights. Consider the following table,...Ch. 5.2 - Pregnancy Lengths. Lengths of pregnancies are...Ch. 5.2 - SAT Scores. Based on data from the College Board,...Ch. 5.2 - GRE Scores. Assume that the scores on the Graduate...Ch. 5.2 - Body Temperatures. Assume that body temperatures...Ch. 5.2 - Spelling Bee Scores. At the district spelling bee,...Ch. 5.2 - Being a Marine. Heights of adult American males...Ch. 5.2 - Prob. 44ECh. 5.3 - Distribution of Means. What is a distribution of...Ch. 5.3 - Notation. This section includes formulas using the...Ch. 5.3 - Central Limit Theorem. What is the Central Limit...Ch. 5.3 - Central Limit Theorem. Briefly explain a major...Ch. 5.3 - Prob. 5ECh. 5.3 - Does It Make Sense? For Exercises 58, determine...Ch. 5.3 - Does It Make Sense? For Exercises 58, determine...Ch. 5.3 - Prob. 8ECh. 5.3 - Prob. 9ECh. 5.3 - Weights. Weights of adult males are normally...Ch. 5.3 - Twelve-Sided Dice and the Central Limit Theorem....Ch. 5.3 - Ten-Sided Dice and the Central Limit Theorem....Ch. 5.3 - Weights. In Exercises 1316, assume that weights of...Ch. 5.3 - Weights. In Exercises 1316, assume that weights of...Ch. 5.3 - Weights. In Exercises 1316, assume that weights of...Ch. 5.3 - Weights. In Exercises 1316, assume that weights of...Ch. 5.3 - Amounts of Cola. Assume that cans of cola are...Ch. 5.3 - Designing Strobe Lights. An aircraft strobe light...Ch. 5.3 - Designing Motorcycle Helmets. Engineers must...Ch. 5.3 - Redesign of Ejection Seats. When women first...Ch. 5.3 - Prob. 21ECh. 5.3 - Vending Machines. Currently, quarters have weights...Ch. 5.3 - Aircraft Safety Standards. Federal Aviation...Ch. 5.3 - Prob. 24ECh. 5 - For each of the following situations, state...Ch. 5 - Women have head circumferences that are normally...Ch. 5 - Assume that body temperatures of healthy adults...Ch. 5 - Which of the following statements are correct? a....Ch. 5 - Which of the following is likely to have a...Ch. 5 - Pulse Rates. In Exercises 310, assume that pulse...Ch. 5 - Pulse Rates. In Exercises 310, assume that pulse...Ch. 5 - Pulse Rates. In Exercises 310, assume that pulse...Ch. 5 - Pulse Rates. In Exercises 310, assume that pulse...Ch. 5 - Pulse Rates. In Exercises 310, assume that pulse...Ch. 5 - Pulse Rates. In Exercises 310, assume that pulse...Ch. 5 - Pulse Rates. In Exercises 310, assume that pulse...Ch. 5 - Pulse Rates. In Exercises 310, assume that pulse...
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