Understandable Statistics: Concepts and Methods
12th Edition
ISBN: 9781337119917
Author: Charles Henry Brase, Corrinne Pellillo Brase
Publisher: Cengage Learning
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Chapter 7, Problem 10CRP
For Problems 4–19, categorize each problem according to the parameter being estimated: proportion p, mean μ, difference of means μ1 − μ2, or difference of proportions p1 − p2. Then solve the problem.
Telephone Interviews: Survey How large a sample is needed in Problem 9 if we wish to be 95% confident that the sample percentage of those equating success with personal satisfaction is within 1% of the population percentage? Hint: Use p ≈ 0.52 as a preliminary estimate.
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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 7 Solutions
Understandable Statistics: Concepts and Methods
Ch. 7.1 - In Problems 18, answer true or false. Explain your...Ch. 7.1 - In Problems 18, answer true or false. Explain your...Ch. 7.1 - In Problems 18, answer true or false. Explain your...Ch. 7.1 - In Problems 18, answer true or false. Explain your...Ch. 7.1 - In Problems 18, answer true or false. Explain your...Ch. 7.1 - In Problems 18, answer true or false. Explain your...Ch. 7.1 - In Problems 18, answer true or false. Explain your...Ch. 7.1 - In Problems 18, answer true or false. Explain your...Ch. 7.1 - Critical Thinking Sam computed a 95% confidence...Ch. 7.1 - Critical Thinking Sam computed a 90% confidence...
Ch. 7.1 - Basic Computation: Confidence Interval Suppose x...Ch. 7.1 - Basic Computation: Confidence Interval Suppose x...Ch. 7.1 - Basic Computation: Sample Size Suppose x has a...Ch. 7.1 - Basic Computation: Sample Size Suppose x has a...Ch. 7.1 - Zoology: Hummingbirds Allens hummingbird...Ch. 7.1 - Diagnostic Tests: Uric Acid Overproduction of uric...Ch. 7.1 - Diagnostic Tests: Plasma Volume Total plasma...Ch. 7.1 - Agriculture: Watermelon What price do farmers get...Ch. 7.1 - Prob. 19PCh. 7.1 - Confidence Intervals: Values of A random sample...Ch. 7.1 - Confidence Intervals: Sample Size A random sample...Ch. 7.1 - Ecology: Sand Dunes At wind speeds above 1000...Ch. 7.1 - Prob. 23PCh. 7.1 - Prob. 24PCh. 7.1 - Prob. 25PCh. 7.2 - Use Table 6 of Appendix II to find tc for a 0.95...Ch. 7.2 - Prob. 2PCh. 7.2 - Prob. 3PCh. 7.2 - Prob. 4PCh. 7.2 - Prob. 5PCh. 7.2 - Prob. 6PCh. 7.2 - Prob. 7PCh. 7.2 - Prob. 8PCh. 7.2 - Prob. 9PCh. 7.2 - Prob. 10PCh. 7.2 - Basic Computation: Confidence Interval Suppose x...Ch. 7.2 - Basic Computation: Confidence Interval A random...Ch. 7.2 - In Problems 1319, assume that the population of x...Ch. 7.2 - In Problems 1319, assume that the population of x...Ch. 7.2 - In Problems 1319, assume that the population of x...Ch. 7.2 - In Problems 1319, assume that the population of x...Ch. 7.2 - In Problems 1319, assume that the population of x...Ch. 7.2 - Prob. 18PCh. 7.2 - Prob. 19PCh. 7.2 - Prob. 20PCh. 7.2 - Prob. 21PCh. 7.2 - Prob. 22PCh. 7.2 - Prob. 23PCh. 7.3 - For all these problems, carry at least four digits...Ch. 7.3 - Prob. 2PCh. 7.3 - Prob. 3PCh. 7.3 - Prob. 4PCh. 7.3 - For all these problems, carry at least four digits...Ch. 7.3 - Prob. 6PCh. 7.3 - Prob. 7PCh. 7.3 - Prob. 8PCh. 7.3 - Prob. 9PCh. 7.3 - For all these problems, carry at least four digits...Ch. 7.3 - Prob. 11PCh. 7.3 - Prob. 12PCh. 7.3 - Prob. 13PCh. 7.3 - For all these problems, carry at least four digits...Ch. 7.3 - Prob. 15PCh. 7.3 - Prob. 16PCh. 7.3 - Prob. 17PCh. 7.3 - Prob. 18PCh. 7.3 - Prob. 19PCh. 7.3 - Prob. 20PCh. 7.3 - Prob. 21PCh. 7.3 - Prob. 22PCh. 7.3 - Prob. 23PCh. 7.3 - Prob. 24PCh. 7.3 - Prob. 25PCh. 7.3 - Prob. 26PCh. 7.3 - Prob. 27PCh. 7.3 - Prob. 28PCh. 7.4 - Prob. 1PCh. 7.4 - Prob. 2PCh. 7.4 - Prob. 3PCh. 7.4 - Prob. 4PCh. 7.4 - Prob. 5PCh. 7.4 - Prob. 6PCh. 7.4 - Prob. 7PCh. 7.4 - Prob. 8PCh. 7.4 - Prob. 9PCh. 7.4 - Prob. 10PCh. 7.4 - Prob. 11PCh. 7.4 - Prob. 12PCh. 7.4 - Prob. 13PCh. 7.4 - Prob. 14PCh. 7.4 - Prob. 15PCh. 7.4 - Prob. 16PCh. 7.4 - Answers may vary slightly due to rounding....Ch. 7.4 - Prob. 18PCh. 7.4 - Prob. 19PCh. 7.4 - Prob. 20PCh. 7.4 - Prob. 21PCh. 7.4 - Prob. 22PCh. 7.4 - Prob. 23PCh. 7.4 - Prob. 24PCh. 7.4 - Prob. 25PCh. 7.4 - Prob. 26PCh. 7.4 - Prob. 27PCh. 7.4 - Prob. 28PCh. 7.4 - Prob. 29PCh. 7.4 - Prob. 30PCh. 7.4 - Prob. 31PCh. 7 - Prob. 1CRPCh. 7 - Critical Thinking Suppose you are told that a 95%...Ch. 7 - Prob. 3CRPCh. 7 - Prob. 4CRPCh. 7 - Prob. 5CRPCh. 7 - For Problems 419, categorize each problem...Ch. 7 - Prob. 7CRPCh. 7 - For Problems 419, categorize each problem...Ch. 7 - Prob. 9CRPCh. 7 - For Problems 419, categorize each problem...Ch. 7 - For Problems 419, categorize each problem...Ch. 7 - For Problems 419, categorize each problem...Ch. 7 - Prob. 13CRPCh. 7 - Prob. 14CRPCh. 7 - Prob. 15CRPCh. 7 - For Problems 419, categorize each problem...Ch. 7 - Prob. 17CRPCh. 7 - Prob. 18CRPCh. 7 - Prob. 19CRPCh. 7 - Prob. 1DHCh. 7 - Prob. 2DHCh. 7 - Prob. 3DHCh. 7 - Prob. 1LCCh. 7 - Prob. 2LCCh. 7 - Prob. 3LCCh. 7 - Prob. 1UT
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