Introduction to Statistics and Data Analysis
5th Edition
ISBN: 9781305115347
Author: Roxy Peck; Chris Olsen; Jay L. Devore
Publisher: Brooks Cole
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Chapter 9.1, Problem 1E
Three different statistics are being considered for estimating a population characteristic. The sampling distributions of the three statistics are shown in the following illustration:
Which statistic would you recommend? Explain your choice. (Hint: See the section on choosing a statistic.)
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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 9 Solutions
Introduction to Statistics and Data Analysis
Ch. 9.1 - Three different statistics are being considered...Ch. 9.1 - a. Why is an unbiased statistic generally...Ch. 9.1 - Prob. 3ECh. 9.1 - Prob. 4ECh. 9.1 - Each person in a random sample of 20 students at a...Ch. 9.1 - Suppose that each of 935 smokers received a...Ch. 9.1 - Given below are the sodium contents (in mg) for...Ch. 9.1 - A random sample of n = 12 four-year-old red pine...Ch. 9.1 - A random sample of 10 houses heated with natural...Ch. 9.2 - Prob. 10E
Ch. 9.2 - The formula used to calculate a large-sample...Ch. 9.2 - Prob. 12ECh. 9.2 - Discuss how each of the following factors affects...Ch. 9.2 - Prob. 14ECh. 9.2 - Based on data from a survey of 1200 randomly...Ch. 9.2 - Prob. 16ECh. 9.2 - If a hurricane was headed your way, would you...Ch. 9.2 - Prob. 18ECh. 9.2 - Prob. 19ECh. 9.2 - Prob. 20ECh. 9.2 - Prob. 21ECh. 9.2 - Prob. 22ECh. 9.2 - Prob. 23ECh. 9.2 - Prob. 24ECh. 9.2 - Prob. 25ECh. 9.2 - Prob. 26ECh. 9.2 - Prob. 27ECh. 9.2 - The Gallup Organization conducts an annual survey...Ch. 9.2 - The article Hospitals Dispute Medtronic Data on...Ch. 9.2 - Prob. 30ECh. 9.2 - A discussion of digital ethics appears in the...Ch. 9.2 - In spite of the potential safety hazards, some...Ch. 9.2 - Prob. 33ECh. 9.3 - Given a variable that has at distribution with the...Ch. 9.3 - The formula used to calculate a confidence...Ch. 9.3 - USA TODAY reported that the average amount of...Ch. 9.3 - Samples of two different models of cars were...Ch. 9.3 - Prob. 38ECh. 9.3 - In a study of academic procrastination, the...Ch. 9.3 - Medical research has shown that repeated wrist...Ch. 9.3 - Prob. 41ECh. 9.3 - Prob. 42ECh. 9.3 - Suppose that a random sample of 50 bottles of a...Ch. 9.3 - Prob. 44ECh. 9.3 - The article The Association Between Television...Ch. 9.3 - Prob. 46ECh. 9.3 - Because of safety considerations, in May 2003 the...Ch. 9.3 - Example 9.3 gave the following airborne times (in...Ch. 9.3 - Prob. 49ECh. 9.3 - Five students visiting the student health center...Ch. 9.3 - The Bureau of Alcohol, Tobacco, and Firearms...Ch. 9.3 - The formula described in this section for...Ch. 9.4 - The following quote is from the article Credit...Ch. 9.4 - Authors of the news release titled Major Gaps...Ch. 9.4 - The paper The Curious Promiscuity of Queen Honey...Ch. 9 - Prob. 56CRCh. 9 - Prob. 57CRCh. 9 - Prob. 58CRCh. 9 - Prob. 59CRCh. 9 - Prob. 60CRCh. 9 - Prob. 61CRCh. 9 - A manufacturer of small appliances purchases...Ch. 9 - Prob. 63CRCh. 9 - A manufacturer of college textbooks is interested...Ch. 9 - Prob. 65CRCh. 9 - The confidence intervals presented in this chapter...Ch. 9 - Prob. 67CRCh. 9 - The interval from 2.33 to 1.75 captures an area of...Ch. 9 - Prob. 69CR
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