MyLab Statistics with Pearson eText -- Standalone Access Card -- for Elementary Statistics Using Excel (My Stat Lab)
6th Edition
ISBN: 9780134748849
Author: Mario F. Triola
Publisher: PEARSON
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Chapter 2.1, Problem 4BSC
To determine
To identify: The two major flaws in the frequency distribution of heights of males.
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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 2 Solutions
MyLab Statistics with Pearson eText -- Standalone Access Card -- for Elementary Statistics Using Excel (My Stat Lab)
Ch. 2.1 - 1. McDonald’s Dinner Service Times Refer 10 the...Ch. 2.1 - Prob. 2BSCCh. 2.1 - Prob. 3BSCCh. 2.1 - Prob. 4BSCCh. 2.1 - In Exercise 5–8, identify the class width, class...Ch. 2.1 - Prob. 6BSCCh. 2.1 - Prob. 7BSCCh. 2.1 - Prob. 8BSCCh. 2.1 - Prob. 9BSCCh. 2.1 - Prob. 10BSC
Ch. 2.1 - Constructing Frequency Distributions. In Exercises...Ch. 2.1 - Constructing Frequency Distributions. In Exercises...Ch. 2.1 - Constructing Frequency Distributions. In Exercises...Ch. 2.1 - 14. Burger King Dinner Service Times Refer to Data...Ch. 2.1 - 15. Wendy’s Lunch Service Times Refer to Data Set...Ch. 2.1 - 16. Wendy’s Dinner Service Times Refer to Data Set...Ch. 2.1 - 17. Analysis of Last Digits Heights of statistics...Ch. 2.1 - 18. Analysis of Last Digits Weights of respondents...Ch. 2.1 - Prob. 19BSCCh. 2.1 - Prob. 20BSCCh. 2.1 - Prob. 21BSCCh. 2.1 - Prob. 22BSCCh. 2.1 - Categorical Data. In Exercises 23 and 24, use the...Ch. 2.1 - Prob. 24BSCCh. 2.1 - Prob. 25BSCCh. 2.1 - Prob. 26BSCCh. 2.1 - Prob. 27BSCCh. 2.1 - Prob. 28BSCCh. 2.1 - Prob. 29BBCh. 2.2 - 1. Heights Heights of adult males are normally...Ch. 2.2 - Prob. 2BSCCh. 2.2 - Prob. 3BSCCh. 2.2 - Prob. 4BSCCh. 2.2 - Interpreting a Histogram. In Exercises 5–8, answer...Ch. 2.2 - Interpreting a Histogram. In Exercises 5–8, answer...Ch. 2.2 - Interpreting a Histogram. In Exercises 5–8, answer...Ch. 2.2 - Interpreting a Histogram. In Exercises 5–8, answer...Ch. 2.2 - Constructing Histograms. In Exercises 9 –45,...Ch. 2.2 - Constructing Histograms. In Exercises 9–45,...Ch. 2.2 - Tornadoes Use the frequency distribution from...Ch. 2.2 - Constructing Histograms. In Exercises 9–45,...Ch. 2.2 - Tornadoes Use the frequency distribution from...Ch. 2.2 - Constructing Histograms. In Exercises 9–45,...Ch. 2.2 - Prob. 15BSCCh. 2.2 - Prob. 16BSCCh. 2.2 - Prob. 17BBCh. 2.2 - Prob. 18BBCh. 2.3 - 1. Body Temperatures Listed below are body...Ch. 2.3 - 2. Voluntary Response Data If we have a large...Ch. 2.3 - 3. Ethics There are data showing that smoking is...Ch. 2.3 - 4. CVDOT Section 2-1 introduced important...Ch. 2.3 - Pulse Rates Listed below are pulse rates (beats...Ch. 2.3 - Diastolic Blood Pressure Listed below are...Ch. 2.3 - Pulse Rates Refer to the data listed in Exercise...Ch. 2.3 - Diastolic Blood Pressure Refer to the data listed...Ch. 2.3 - Time-Series Graphs. In Exercises 9 and 10,...Ch. 2.3 - Time-Series Graphs. In Exercises 9 and 10,...Ch. 2.3 - Prob. 11BSCCh. 2.3 - Prob. 12BSCCh. 2.3 - Prob. 13BSCCh. 2.3 - Prob. 14BSCCh. 2.3 - Prob. 15BSCCh. 2.3 - Frequency Polygon. In Exercises 15 and 13,...Ch. 2.3 - Prob. 17BSCCh. 2.3 - Deceptive Graphs. In Exercises 17-20, identify how...Ch. 2.3 - Prob. 19BSCCh. 2.3 - Prob. 20BSCCh. 2.3 - Prob. 21BBCh. 2.4 - 1. Linear Correlation In this section we use r to...Ch. 2.4 - Prob. 2BSCCh. 2.4 - Prob. 3BSCCh. 2.4 - 4. Estimating r For each of the following,...Ch. 2.4 - Scatterplot. In Exercises 5 – 8, use the sample...Ch. 2.4 - Prob. 6BSCCh. 2.4 - Scatterplot. In Exercises 5 – 8, use the sample...Ch. 2.4 - Scatterplot. In Exercises 5 – 8, use the sample...Ch. 2.4 - Linear Correlation Coefficient In Exercises 9-12,...Ch. 2.4 - Linear Correlation Coefficient In Exercises 9-12,...Ch. 2.4 - Linear Correlation Coefficient In Exercises 9-12,...Ch. 2.4 - Prob. 12BSCCh. 2.4 - Prob. 13BBCh. 2.4 - Prob. 14BBCh. 2.4 - Prob. 15BBCh. 2.4 - Prob. 16BBCh. 2 - Prob. 1CQQCh. 2 - Prob. 2CQQCh. 2 - Prob. 3CQQCh. 2 - Prob. 4CQQCh. 2 - Prob. 5CQQCh. 2 - Prob. 6CQQCh. 2 - Prob. 7CQQCh. 2 - Prob. 8CQQCh. 2 - Prob. 9CQQCh. 2 - Prob. 10CQQCh. 2 - 1. Frequency Distribution of Body Temperatures...Ch. 2 - Prob. 2RECh. 2 - Prob. 3RECh. 2 - Prob. 4RECh. 2 - Prob. 5RECh. 2 - Prob. 6RECh. 2 - Prob. 7RECh. 2 - Prob. 8RECh. 2 - Prob. 1CRECh. 2 - Prob. 2CRECh. 2 - Histogram Construct the histogram corresponding to...Ch. 2 - Prob. 4CRECh. 2 - Prob. 5CRECh. 2 - Prob. 6CRECh. 2 - Prob. 1EP
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