Introduction To Probability And Statistics
15th Edition
ISBN: 9781337554428
Author: Mendenhall, William.
Publisher: Cengage Learning,
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Textbook Question
Chapter 1.2, Problem 1E
Pie and Bar Charts The data in Exercises 1−3 represent different ways to classify a group of 100 students in a statistics class. Construct a bar chart and pie chart to describe each set of data.
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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 1 Solutions
Introduction To Probability And Statistics
Ch. 1.1 - Experimental UnitsDefine the experimental units...Ch. 1.1 - Experimental UnitsDefine the experimental units...Ch. 1.1 - Experimental UnitsDefine the experimental units...Ch. 1.1 - Experimental UnitsDefine the experimental units...Ch. 1.1 - Experimental UnitsDefine the experimental units...Ch. 1.1 - Qualitative or Quantitative? Are the variables in...Ch. 1.1 - Qualitative or Quantitative? Are the variables in...Ch. 1.1 - Qualitative or Quantitative? Are the variables in...Ch. 1.1 - Qualitative or Quantitative? Are the variables in...Ch. 1.1 - Discrete or Continuous? Are the variables in...
Ch. 1.1 - Discrete or Continuous? Are the variables in...Ch. 1.1 - Discrete or Continuous? Are the variables in...Ch. 1.1 - Discrete or Continuous? Are the variables in...Ch. 1.1 - Discrete or Continuous? Are the variables in...Ch. 1.1 - Discrete or Continuous? Are the variables in...Ch. 1.1 - Discrete or Continuous? Are the variables in...Ch. 1.1 - Discrete or Continuous? Are the variables in...Ch. 1.1 - Discrete or Continuous? Are the variables in...Ch. 1.1 - Populations or Samples? In Exercises 1922,...Ch. 1.1 - Populations or Samples? In Exercises 1922,...Ch. 1.1 - Populations or Samples? In Exercises 1922,...Ch. 1.1 - Populations or Samples? In Exercises 1922,...Ch. 1.1 - Parking on Campus Six vehicles selected from a...Ch. 1.1 - Past U.S. Presidents A data set gives the ages at...Ch. 1.1 - Voter Attitudes You are a candidate for your state...Ch. 1.1 - Cancer Survival Times A researcher wants to...Ch. 1.1 - New Teaching Methods A researcher wants to know...Ch. 1.2 - Pie and Bar Charts The data in Exercises 13...Ch. 1.2 - Pie and Bar Charts The data in Exercises 13...Ch. 1.2 - Pie and Bar Charts The data in Exercises 13...Ch. 1.2 - Groups of People Fifty people are grouped into...Ch. 1.2 - Presidential Popularity After the elections of...Ch. 1.2 - Presidential Popularity After the elections of...Ch. 1.2 - Presidential Popularity After the elections of...Ch. 1.2 - Presidential Popularity After the elections of...Ch. 1.2 - Presidential Popularity After the elections of...Ch. 1.2 - Prob. 10ECh. 1.2 - Prob. 11ECh. 1.2 - Prob. 12ECh. 1.2 - Prob. 13ECh. 1.2 - Prob. 14ECh. 1.2 - Prob. 15ECh. 1.2 - Back to Work How long does it take you to adjust...Ch. 1.2 - Prob. 17ECh. 1.2 - Prob. 18ECh. 1.2 - Prob. 19ECh. 1.2 - Prob. 20ECh. 1.2 - Prob. 21ECh. 1.3 - DotplotsConstruct a dotplot for the data given in...Ch. 1.3 - DotplotsConstruct a dotplot for the data given in...Ch. 1.3 - Stem and Leaf I Construct a stem and leaf plot for...Ch. 1.3 - Stem and Leaf I Construct a stem and leaf plot for...Ch. 1.3 - Stem and Leaf I Construct a stem and leaf plot for...Ch. 1.3 - Stem and Leaf II Use the following set of data...Ch. 1.3 - Stem and Leaf II Use the following set of data...Ch. 1.3 - Prob. 8ECh. 1.3 - Prob. 9ECh. 1.3 - Comparing Graphs A discrete variable can take on...Ch. 1.3 - Prob. 11ECh. 1.3 - Prob. 12ECh. 1.3 - Prob. 13ECh. 1.3 - Prob. 14ECh. 1.3 - Prob. 15ECh. 1.3 - Prob. 16ECh. 1.3 - Prob. 17ECh. 1.3 - Calcium Contents The calcium content (Ca)of a...Ch. 1.3 - Prob. 19ECh. 1.3 - Prob. 20ECh. 1.3 - Prob. 21ECh. 1.3 - Prob. 22ECh. 1.3 - Prob. 23ECh. 1.3 - Prob. 24ECh. 1.3 - American Presidents The following table lists the...Ch. 1.4 - Graphing Relative Frequency Histograms Construct a...Ch. 1.4 - Graphing Relative Frequency Histograms Construct a...Ch. 1.4 - Interpreting Relative Frequency Histograms Use the...Ch. 1.4 - Interpreting Relative Frequency Histograms Use the...Ch. 1.4 - Interpreting Relative Frequency Histograms Use the...Ch. 1.4 - Interpreting Relative Frequency Histograms Use the...Ch. 1.4 - Interpreting Relative Frequency Histograms Use the...Ch. 1.4 - Interpreting Relative Frequency Histograms Use the...Ch. 1.4 - Class Boundaries In Exercises 912, use the...Ch. 1.4 - Class Boundaries In Exercises 912, use the...Ch. 1.4 - Prob. 11ECh. 1.4 - Prob. 12ECh. 1.4 - Prob. 13ECh. 1.4 - Prob. 14ECh. 1.4 - Relative Frequency Histogram I Construct a...Ch. 1.4 - Prob. 16ECh. 1.4 - Prob. 17ECh. 1.4 - Prob. 18ECh. 1.4 - Prob. 19ECh. 1.4 - Prob. 20ECh. 1.4 - Prob. 21ECh. 1.4 - Prob. 22ECh. 1.4 - Prob. 23ECh. 1.4 - Prob. 24ECh. 1.4 - A Recurring Illness The length of time (in months)...Ch. 1.4 - Prob. 26ECh. 1.4 - Prob. 27ECh. 1.4 - Prob. 28ECh. 1.4 - Prob. 29ECh. 1.4 - Prob. 30ECh. 1.4 - Prob. 31ECh. 1.4 - Student Heights The self-reported heights of 105...Ch. 1.4 - Prob. 33ECh. 1 - Quantitative or Qualitative? Identify each...Ch. 1 - Symmetric or Skewed? Do you expect the...Ch. 1 - Continuous or Discrete? Identify each variable as...Ch. 1 - Continuous or Discrete, again Identify each...Ch. 1 - World Lakes A lake is a body of water surrounded...Ch. 1 - Prob. 6RWYLCh. 1 - Election Results The 2016 election was a race in...Ch. 1 - Prob. 8RWYLCh. 1 - Prob. 9RWYLCh. 1 - Pulse Rates A group of 50 biomedical students...Ch. 1 - Prob. 11RWYLCh. 1 - Prob. 12RWYLCh. 1 - Gasoline Tax The following are the 2017 state...Ch. 1 - Prob. 14RWYLCh. 1 - Prob. 15RWYLCh. 1 - Prob. 16RWYLCh. 1 - Kentucky Derby The following data set shows the...Ch. 1 - Prob. 18RWYLCh. 1 - Old Faithful The following data are the waiting...Ch. 1 - Prob. 20RWYLCh. 1 - Prob. 1CSCh. 1 - Prob. 2CS
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