Introductory Statistics (2nd Edition)
2nd Edition
ISBN: 9780321978271
Author: Robert Gould, Colleen N. Ryan
Publisher: PEARSON
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Chapter 11, Problem 4SE
a.
To determine
Determine and list the number of pairwise comparisons that can be done with four groups.
b.
To determine
Determine the significance level that should be used for each hypothesis test for overall significance level of 0.05.
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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 11 Solutions
Introductory Statistics (2nd Edition)
Ch. 11 - Choosing a Test a. You wish to test whether an...Ch. 11 - Prob. 2SECh. 11 - Bonferroni Correction (Example 1) Suppose you have...Ch. 11 - Prob. 4SECh. 11 - Prob. 5SECh. 11 - Prob. 6SECh. 11 - Prob. 7SECh. 11 - Prob. 8SECh. 11 - Prob. 9SECh. 11 - Prob. 10SE
Ch. 11 - Gas Price Intervals Use the data from exercise...Ch. 11 - Gas Price Intervals Use the data from exercise...Ch. 11 - Work Hours and Education The table shows the...Ch. 11 - Prob. 14SECh. 11 - Comparing F -Values from Boxplots (Example 3)...Ch. 11 - Comparing F -Values from Boxplots Refer to the...Ch. 11 - Marital Status and Cholesterol (Example 4) Refer...Ch. 11 - Marital Status and Blood Pressure Test the...Ch. 11 - Schoolwork and Class (Example 5) A random survey...Ch. 11 - TV Hours A random survey was done at a small...Ch. 11 - Schoolwork and Class Use the information for...Ch. 11 - TV Hours Use the information for exercise 11.20....Ch. 11 - Schoolwork Again Go back to the information in...Ch. 11 - TV Hours Again Go back to the information in...Ch. 11 - Pulse Rates (Example 6) Pulse rates were taken for...Ch. 11 - UCLA Music Survey The figure shows side-by-side...Ch. 11 - Commute Times by Method A survey was given to...Ch. 11 - Prob. 30SECh. 11 - Prob. 31SECh. 11 - Study Hours by Major Three independent random...Ch. 11 - Salary by Type of College Information was gathered...Ch. 11 - Draft Lottery When the draft lottery for military...Ch. 11 - Reaction Times for Athletes A random sample of...Ch. 11 - Tomato Plants and Colored Light Jennifer Brogan, a...Ch. 11 - GPAs by Seating Choice A random sample of students...Ch. 11 - Reading Comprehension Sixty-six reading students...Ch. 11 - Hours of Steep and Health Status In a study done...Ch. 11 - Happiness and Age Category StatCrunch surveyed...Ch. 11 - Prob. 41SECh. 11 - House Prices Tukey HSD confidence intervals (with...Ch. 11 - GPA and Row (Example 8) A random sample of...Ch. 11 - Reading Scores by Teaching Method Refer to...Ch. 11 - Reaction Distances Use the data given in exercise...Ch. 11 - Study Hours Use the data given in exercise 11.32....Ch. 11 - Baseball Player Run-Times (Example 9) Determine...Ch. 11 - Tomatoes Use the data given in exercise 11.36....Ch. 11 - Concern over Nuclear Power Following the...Ch. 11 - Immigration Issue A survey was done by StatCrunch...Ch. 11 - Happiness and Age Consider the data from the...Ch. 11 - GPA and Row Number Suppose you collect data on...Ch. 11 - Contacting Mother Professors of ethics (Eth),...Ch. 11 - Ideal Percentage to Charity Professors of ethics...Ch. 11 - Actual Percentage to Charity Professors of ethics...Ch. 11 - Hours of Television by Age Group The StatCrunch...Ch. 11 - Triglycerides and Gender Using the NHANES data, we...Ch. 11 - Cholesterol and Gender Using NHANES data, we...
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