Statistical Reasoning for Everyday Life - MyStatLab
5th Edition
ISBN: 9781323823781
Author: Bennett
Publisher: PEARSON
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Chapter 3.3, Problem 24E
Creating Graphics. Exercises 23–26 give tables of real data. For each table, construct a graphical display of the data. Choose any graphic type that you feel is appropriate to the data set. In addition to constructing the graph, explain why you chose this type of display and describe interesting patterns in the data.
24. Daily Newspapers. The following table gives the number of daily newspapers and their total circulation (in millions) for selected years since 1920 (from Editor & Publisher).
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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 3 Solutions
Statistical Reasoning for Everyday Life - MyStatLab
Ch. 3.1 - Frequency Table. What is a frequency table? How...Ch. 3.1 - Relative Frequency. What do we mean by relative...Ch. 3.1 - Cumulative Frequency. What do we mean by...Ch. 3.1 - Binning. What is the purpose of binning? Give an...Ch. 3.1 - Does It Make Sense? For Exercises 58, determine...Ch. 3.1 - Does It Make Sense? For Exercises 58, determine...Ch. 3.1 - Does It Make Sense? For Exercises 58, determine...Ch. 3.1 - Does It Make Sense? For Exercises 58, determine...Ch. 3.1 - Pulse Rates of Females. In Exercises 912, refer to...Ch. 3.1 - Pulse Rates of Females. In Exercises 912, refer to...
Ch. 3.1 - Pulse Rates of Females. In Exercises 912, refer to...Ch. 3.1 - Pulse Rates of Females. In Exercises 912, refer to...Ch. 3.1 - Birth Days. Births at a hospital in New York State...Ch. 3.1 - Clinical Trial. As part of a clinical trial, the...Ch. 3.1 - Train Derailments. An analysis of 50 train...Ch. 3.1 - Analysis of Last Digits. Weights of respondents...Ch. 3.1 - Academy Award-Winning Male Actors. The following...Ch. 3.1 - Body Temperatures. The following data show the...Ch. 3.1 - Loaded Die. An experiment was conducted in which a...Ch. 3.1 - Interpreting Family Data. Consider the following...Ch. 3.1 - Computer Keyboards. The traditional keyboard...Ch. 3.1 - Double Binning. The students in a statistics class...Ch. 3.2 - Distribution Graph. What is a distribution of...Ch. 3.2 - Qualitative Data. Which types of graph described...Ch. 3.2 - Yearly Data. Which type of graph described in this...Ch. 3.2 - Histogram and Stemplot. Assume that a data set is...Ch. 3.2 - Prob. 5ECh. 3.2 - Does It Make Sense? For Exercises 58, determine...Ch. 3.2 - Does It Make Sense? For Exercises 58, determine...Ch. 3.2 - Does It Make Sense? For Exercises 58, determine...Ch. 3.2 - Histogram. Children living near a smelter in Texas...Ch. 3.2 - Understanding Data. Suppose you have a list of...Ch. 3.2 - Most Appropriate Display. Exercises 1114 describe...Ch. 3.2 - Most Appropriate Display. Exercises 1114 describe...Ch. 3.2 - Most Appropriate Display. Exercises 1114 describe...Ch. 3.2 - Most Appropriate Display. Exercises 1114 describe...Ch. 3.2 - Academy Award-Winning Male Actors. Exercise 17 in...Ch. 3.2 - Body Temperatures. Exercise 18 in Section 3.1...Ch. 3.2 - Job Hunting. A survey was conducted to determine...Ch. 3.2 - Job Hunting. Refer to the data given in Exercise...Ch. 3.2 - Prob. 19ECh. 3.2 - Job Application Mistakes Construct a Pareto chart...Ch. 3.2 - Dotplot. Refer to the QWERTY data in Exercise 21...Ch. 3.2 - Dotplot. Refer to the Dvorak data in Exercise 21...Ch. 3.2 - Stemplot. Construct a stemplot of these test...Ch. 3.2 - Stemplot. Listed below are the lengths (in...Ch. 3.2 - DJIA. Listed below (in order by row) are annual...Ch. 3.2 - Home Runs. Listed below (in order by row) are the...Ch. 3.3 - Multiple Data. Briefly describe how each of the...Ch. 3.3 - Prob. 2ECh. 3.3 - Prob. 3ECh. 3.3 - Prob. 4ECh. 3.3 - Does It Make Sense? For Exercises 58, determine...Ch. 3.3 - Does It Make Sense? For Exercises 58, determine...Ch. 3.3 - Does It Make Sense? For Exercises 58, determine...Ch. 3.3 - Does It Make Sense? For Exercises 58, determine...Ch. 3.3 - Public and Private Colleges. The stack plot in...Ch. 3.3 - Home Prices by Region. The graph in Figure 3.21...Ch. 3.3 - Gender and Salary. Consider the display in Figure...Ch. 3.3 - Marriage and Divorce Rates. The graph in Figure...Ch. 3.3 - Prob. 13ECh. 3.3 - College Degrees. The stack plot in Figure 3.25...Ch. 3.3 - Contour Map. For Exercises 17 and 18, refer to the...Ch. 3.3 - Prob. 18ECh. 3.3 - Prob. 19ECh. 3.3 - Prob. 20ECh. 3.3 - Infographic. For Exercises 21 and 22, refer to...Ch. 3.3 - Infographic. For Exercises 21 and 22, refer to...Ch. 3.3 - Creating Graphics. Exercises 2326 give tables of...Ch. 3.3 - Creating Graphics. Exercises 2326 give tables of...Ch. 3.3 - Firearms Fatalities. The following table...Ch. 3.3 - Prob. 26ECh. 3.4 - Perceptual Distortion. Use a ruler to measure the...Ch. 3.4 - Prob. 2ECh. 3.4 - Prob. 3ECh. 3.4 - Prob. 4ECh. 3.4 - Does It Make Sense? For Exercises 58, determine...Ch. 3.4 - Does It Make Sense? For Exercises 58, determine...Ch. 3.4 - Does It Make Sense? For Exercises 58, determine...Ch. 3.4 - Does It Make Sense? For Exercises 58, determine...Ch. 3.4 - Exaggerating a Difference. Weekly instruction time...Ch. 3.4 - Graph of Sounds. In a survey conducted by Kelton...Ch. 3.4 - Graph Dimensions. A newspaper used images of...Ch. 3.4 - Prob. 12ECh. 3.4 - Prob. 13ECh. 3.4 - DJIA. Figure 3.36 on the next page depicts the...Ch. 3.4 - Prob. 15ECh. 3.4 - Prob. 16ECh. 3.4 - Prob. 17ECh. 3.4 - Moores Law. In 1965, Intel cofounder Gordon Moore...Ch. 3.4 - Prob. 19ECh. 3.4 - Prob. 20ECh. 3.4 - Constant Dollars. The graph in Figure 3.41 shows...Ch. 3.4 - Prob. 22ECh. 3 - Listed below are measured weights (in pounds) of...Ch. 3 - Listed below are measured weights (in pounds) of...Ch. 3 - Listed below are measured weights (in pounds) of...Ch. 3 - Pie Chart for Sports Equipment. USA Today reported...Ch. 3 - Pareto Chart for Sports Equipment. Construct a...Ch. 3 - Bar Chart. Figure 3.43 shows the numbers of U.S....Ch. 3 - As a quality control manager at Ford Motor...Ch. 3 - As a quality control manager at Ford, you monitor...Ch. 3 - A stemplot is created with the braking distances...Ch. 3 - A dotplot of braking distances (in feet) of cars...Ch. 3 - The first category in a frequency table is 90100,...Ch. 3 - The first category in a relative frequency table...Ch. 3 - The third category in a frequency table has a...Ch. 3 - Prob. 8CQCh. 3 - When constructing a graph of the same categorical...Ch. 3 - Body Temperatures Listed below are body...Ch. 3 - Why are pictographs generally poor for depicting...Ch. 3 - Note that this graph plots six variables: two...Ch. 3 - Prob. 2.2FCh. 3 - Prob. 2.3F
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