Elementary Statistics: Picturing the World (6th Edition)
6th Edition
ISBN: 9780321911216
Author: Ron Larson, Betsy Farber
Publisher: PEARSON
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Chapter 10.4, Problem 16E
To determine
To interpret: The results of two-way ANOVA test with level of significance 0.10.
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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 10 Solutions
Elementary Statistics: Picturing the World (6th Edition)
Ch. 10.1 - Prob. 1TYCh. 10.1 - Prob. 2TYCh. 10.1 - Prob. 3TYCh. 10.1 - What is a multinomial experiment?Ch. 10.1 - What conditions are necessary to use the...Ch. 10.1 - Finding Expected Frequencies In Exercises 36, find...Ch. 10.1 - Finding Expected Frequencies In Exercises 36, find...Ch. 10.1 - Finding Expected Frequencies In Exercises 36, find...Ch. 10.1 - Finding Expected Frequencies In Exercises 36, find...Ch. 10.1 - Prob. 7E
Ch. 10.1 - Prob. 8ECh. 10.1 - Performing a Chi-Square Goodness-of-Fit Test In...Ch. 10.1 - Prob. 10ECh. 10.1 - Prob. 11ECh. 10.1 - Prob. 12ECh. 10.1 - Performing a Chi-Square Goodness-of-Fit Test In...Ch. 10.1 - Performing a Chi-Square Goodness-of-Fit Test In...Ch. 10.1 - Performing a Chi-Square Goodness-of-Fit Test In...Ch. 10.1 - Prob. 16ECh. 10.1 - In Exercises 17 and 18, (a) find the expected...Ch. 10.1 - In Exercises 17 and 18, (a) find the expected...Ch. 10.2 - Prob. 1TYCh. 10.2 - Prob. 2TYCh. 10.2 - Prob. 3TYCh. 10.2 - Prob. 1ECh. 10.2 - Explain the difference between marginal...Ch. 10.2 - Prob. 3ECh. 10.2 - Prob. 4ECh. 10.2 - Prob. 5ECh. 10.2 - True or False? In Exercises 5 and 6, determine...Ch. 10.2 - Finding Expected Frequencies In Exercises 712, (a)...Ch. 10.2 - Finding Expected Frequencies In Exercises 712, (a)...Ch. 10.2 - Prob. 9ECh. 10.2 - Prob. 10ECh. 10.2 - Prob. 11ECh. 10.2 - Prob. 12ECh. 10.2 - Performing a Chi-Square Independence Test In...Ch. 10.2 - Performing a Chi-Square Independence Test In...Ch. 10.2 - Performing a Chi-Square Independence Test In...Ch. 10.2 - Prob. 16ECh. 10.2 - Prob. 17ECh. 10.2 - Performing a Chi-Square Independence Test In...Ch. 10.2 - Prob. 19ECh. 10.2 - Prob. 20ECh. 10.2 - Prob. 21ECh. 10.2 - Prob. 22ECh. 10.2 - Prob. 23ECh. 10.2 - Prob. 24ECh. 10.2 - Prob. 25ECh. 10.2 - Prob. 26ECh. 10.2 - Prob. 27ECh. 10.2 - Prob. 28ECh. 10.2 - Prob. 29ECh. 10.2 - Prob. 30ECh. 10.2 - Prob. 31ECh. 10.2 - Prob. 32ECh. 10.2 - Prob. 33ECh. 10.2 - Prob. 34ECh. 10.2 - Prob. 35ECh. 10.2 - In your opinion, how safe is the food you buy? CBS...Ch. 10.2 - In your opinion, how safe is the food you buy? CBS...Ch. 10.2 - In your opinion, how safe is the food you buy? CBS...Ch. 10.2 - In your opinion, how safe is the food you buy? CBS...Ch. 10.2 - In your opinion, how safe is the food you buy? CBS...Ch. 10.2 - In your opinion, how safe is the food you buy? CBS...Ch. 10.3 - Prob. 1TYCh. 10.3 - Prob. 2TYCh. 10.3 - Prob. 3TYCh. 10.3 - Prob. 4TYCh. 10.3 - Explain how to find the critical value for an...Ch. 10.3 - List five properties of the F-distribution.Ch. 10.3 - List the three conditions that must be met in...Ch. 10.3 - Explain how to determine the values of d.f.N and...Ch. 10.3 - Prob. 5ECh. 10.3 - Prob. 6ECh. 10.3 - Prob. 7ECh. 10.3 - Finding a Critical F-Value for a Right-Tailed Test...Ch. 10.3 - Prob. 9ECh. 10.3 - Finding a Critical F-Value for a Right-Tailed Test...Ch. 10.3 - Finding a Critical F-Value for a Right-Tailed Test...Ch. 10.3 - Finding a Critical F-Value for a Right-Tailed Test...Ch. 10.3 - In Exercises 1318, test the claim about the...Ch. 10.3 - In Exercises 1318, test the claim about the...Ch. 10.3 - Prob. 15ECh. 10.3 - Prob. 16ECh. 10.3 - Prob. 17ECh. 10.3 - In Exercises 1318, test the claim about the...Ch. 10.3 - Performing a Two-Sample F-Test In Exercises 1926,...Ch. 10.3 - Prob. 20ECh. 10.3 - Prob. 21ECh. 10.3 - Performing a Two-Sample F-Test In Exercises 1926,...Ch. 10.3 - Performing a Two-Sample F-Test In Exercises 1926,...Ch. 10.3 - Prob. 24ECh. 10.3 - Prob. 25ECh. 10.3 - Performing a Two-Sample F-Test In Exercises 1926,...Ch. 10.3 - Prob. 27ECh. 10.3 - In Exercises 27 and 28, find the right- and...Ch. 10.3 - In Exercises 29 and 30, construct the confidence...Ch. 10.3 - In Exercises 29 and 30, construct the confidence...Ch. 10.4 - Prob. 1TYCh. 10.4 - Prob. 2TYCh. 10.4 - Slate the null and alternative hypotheses for a...Ch. 10.4 - What conditions are necessary in order to use a...Ch. 10.4 - Describe the difference between the variance...Ch. 10.4 - Prob. 4ECh. 10.4 - Performing a One-Way ANOVA Test In Exercises 514,...Ch. 10.4 - Prob. 6ECh. 10.4 - Prob. 7ECh. 10.4 - Prob. 8ECh. 10.4 - Prob. 9ECh. 10.4 - Prob. 10ECh. 10.4 - Prob. 11ECh. 10.4 - Prob. 12ECh. 10.4 - Prob. 13ECh. 10.4 - Prob. 14ECh. 10.4 - Prob. 15ECh. 10.4 - Prob. 16ECh. 10.4 - Prob. 17ECh. 10.4 - Prob. 18ECh. 10.4 - The Scheff Test If the null hypothesis is rejected...Ch. 10.4 - Prob. 20ECh. 10.4 - Prob. 21ECh. 10.4 - Prob. 22ECh. 10 - In Exercises 14. (a) identify the claim and state...Ch. 10 - Prob. 10.1.2RECh. 10 - In Exercises 14, (a) identify the claim and state...Ch. 10 - Prob. 10.1.4RECh. 10 - Prob. 10.2.5RECh. 10 - Prob. 10.2.6RECh. 10 - Prob. 10.2.7RECh. 10 - Prob. 10.2.8RECh. 10 - Prob. 10.3.9RECh. 10 - Prob. 10.3.10RECh. 10 - Prob. 10.3.11RECh. 10 - Prob. 10.3.12RECh. 10 - Prob. 10.3.13RECh. 10 - Prob. 10.3.14RECh. 10 - Prob. 10.3.15RECh. 10 - Prob. 10.3.16RECh. 10 - Prob. 10.3.17RECh. 10 - Prob. 10.3.18RECh. 10 - Prob. 10.3.19RECh. 10 - Prob. 10.3.20RECh. 10 - Prob. 10.4.21RECh. 10 - Prob. 10.4.22RECh. 10 - Prob. 1CQCh. 10 - Prob. 2CQCh. 10 - Prob. 3CQCh. 10 - Prob. 4CQCh. 10 - Prob. 1CTCh. 10 - Prob. 2CTCh. 10 - Prob. 3CTCh. 10 - Prob. 4CTCh. 10 - Prob. 5CTCh. 10 - Prob. 6CTCh. 10 - Prob. 1RSRDCh. 10 - Independence The contingency table below shows the...Ch. 10 - Prob. 1TCh. 10 - Prob. 2TCh. 10 - Prob. 3TCh. 10 - Prob. 4TCh. 10 - Prob. 5TCh. 10 - Prob. 1CRCh. 10 - Prob. 2CRCh. 10 - Prob. 3CRCh. 10 - Prob. 4CRCh. 10 - Prob. 5CRCh. 10 - Reviewing a Movie The contingency table shows how...Ch. 10 - Prob. 7CR
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