
Elementary Statistics 2nd Edition
2nd Edition
ISBN: 9781259724275
Author: William Navidi, Barry Monk
Publisher: McGraw-Hill Education
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Question
Chapter 3, Problem 4RE
a)
To determine
To find sample variance of the thicknesses for each process.
b)
To determine
To find Sample standard deviation of each process.
c)
To determine
To find which process appears to be better in producing a uniform thickness.
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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
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Erickson
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Francis
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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 3 Solutions
Elementary Statistics 2nd Edition
Ch. 3.1 - In Exercises 9—12, fill in each blank with the...Ch. 3.1 - In Exercises 9—12, fill in each blank with the...Ch. 3.1 - In Exercises 9—12, fill in each blank with the...Ch. 3.1 - In Exercises 9—12, fill in each blank with the...Ch. 3.1 - In Exercises 13—16, determine whether the...Ch. 3.1 - In Exercises 13—16, determine whether the...Ch. 3.1 - In Exercises 13—16, determine whether the...Ch. 3.1 - In Exercises 13—16, determine whether the...Ch. 3.1 - Find the mean, median, and mode for the following...Ch. 3.1 - Find the mean, median, and mode for the following...
Ch. 3.1 - Find the mean, median, and mode for the following...Ch. 3.1 - Find the mean, median, and mode for the following...Ch. 3.1 - Prob. 19ECh. 3.1 - In Exercises 21—24, use the given frequency...Ch. 3.1 - In Exercises 21—24, use the given frequency...Ch. 3.1 - In Exercises 21—24, use the given frequency...Ch. 3.1 - Use the properties of the mean and median to...Ch. 3.1 - Use the properties of the mean and median to...Ch. 3.1 - Use the properties of the mean and median to...Ch. 3.1 - Use the properties of the mean and median to...Ch. 3.1 - Find the mean, median, and mode of the data in the...Ch. 3.1 - Find the mean, median, and mode of the data in the...Ch. 3.1 - Facebook friends: In a study of Facebook users...Ch. 3.1 - Mean and median height: The National Center for...Ch. 3.1 - Prob. 31ECh. 3.1 - Greater swimmer: In the 2008 OIympic Games. Michel...Ch. 3.1 - Prob. 33ECh. 3.1 - Prob. 34ECh. 3.1 - Prob. 35ECh. 3.1 - Prob. 36ECh. 3.1 - Prob. 37ECh. 3.1 - Prob. 38ECh. 3.1 - Heavy football players: Following are the weights,...Ch. 3.1 - Prob. 40ECh. 3.1 - Flu season: The following table presents the...Ch. 3.1 - News flash: The following table presents the...Ch. 3.1 - Commercial bank: Following arc amounts spend (in...Ch. 3.1 - Prob. 44ECh. 3.1 - Dont drink and drive: The Insurance Institute for...Ch. 3.1 - Prob. 46ECh. 3.1 - Be my Valentine: The following frequency...Ch. 3.1 - Get your degree: The following frequency...Ch. 3.1 - Prob. 49ECh. 3.1 - Take in a show: The following table presents the...Ch. 3.1 - Prob. 51ECh. 3.1 - Sources of news: A sample of 32 U.S. adults was...Ch. 3.1 - Find the mean: The National Center for Health...Ch. 3.1 - Find the median: According to a recent Current...Ch. 3.1 - Find the median: In a recent year, approximately...Ch. 3.1 - Find the median: The National Health and Nutrition...Ch. 3.1 - Prob. 57ECh. 3.1 - Prob. 58ECh. 3.1 - How many numbers? A data set has a median of 17,...Ch. 3.1 - Prob. 60ECh. 3.1 - Prob. 61ECh. 3.1 - Prob. 62ECh. 3.1 - Prob. 63ECh. 3.1 - Prob. 64ECh. 3.1 - Prob. 65ECh. 3.1 - Prob. 66ECh. 3.1 - Prob. 67ECh. 3.1 - Prob. 68ECh. 3.1 - Prob. 69ECh. 3.1 - Prob. 70ECh. 3.1 - Prob. 71ECh. 3.1 - Prob. 72ECh. 3.1 - Prob. 73ECh. 3.1 - Prob. 74ECh. 3.2 - In Exercises 11—14, fill in each blank with the...Ch. 3.2 - In Exercises 11—14, fill in each blank with the...Ch. 3.2 - In Exercises 11—14, fill in each blank with the...Ch. 3.2 - In Exercises 11—14, fill in each blank with the...Ch. 3.2 - In Exercises 15—18, determine whether the...Ch. 3.2 - In Exercises 15—18, determine whether the...Ch. 3.2 - In Exercises 15—18, determine whether the...Ch. 3.2 - In Exercises 15—18, determine whether the...Ch. 3.2 - Find the sample variance and standard deviation...Ch. 3.2 - Find the sample variance and standard deviation...Ch. 3.2 - Find the sample variance and standard deviation...Ch. 3.2 - Find the population variance and standard...Ch. 3.2 - Find the population variance and standard...Ch. 3.2 - Find the population variance and standard...Ch. 3.2 - Approximate the sample variance and standard...Ch. 3.2 - Approximate the sample variance and standard...Ch. 3.2 - Approximate the population variance and standard...Ch. 3.2 - Approximate the population variance and standard...Ch. 3.2 - Prob. 27ECh. 3.2 - Prob. 28ECh. 3.2 - Prob. 29ECh. 3.2 - Prob. 30ECh. 3.2 - Prob. 31ECh. 3.2 - Sports car or convertible? 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The following histogram...Ch. 3.2 - Empirical Rule OK? The following histogram...Ch. 3.2 - Empirical Rule OK? The following histogram...Ch. 3.2 - Whats the temperature? The temperature in a...Ch. 3.2 - Find the standard deviation: The National Center...Ch. 3.2 - Find the standard deviation: The National Center...Ch. 3.2 - Price of electricity: The Energy Information...Ch. 3.2 - Possible or impossible? A data set has a mean of...Ch. 3.2 - Possible or impossible? A data set has a mean of...Ch. 3.2 - Prob. 59ECh. 3.2 - Prob. 60ECh. 3.2 - Height and weight: A Naona1 Center for Health...Ch. 3.2 - Test scores: Scores on a statistics exam had a...Ch. 3.2 - Mean absolute deviation: A measure of spread that...Ch. 3.3 - In Exercises 9—12, fill in each blank with the...Ch. 3.3 - In Exercises 9—12, fill in each blank with the...Ch. 3.3 - In Exercises 9—12, fill in each blank with the...Ch. 3.3 - In Exercises 9—12, fill in each blank with the...Ch. 3.3 - In Exercises 13—16, determine whether the...Ch. 3.3 - In Exercises 13—16, determine whether the...Ch. 3.3 - In Exercises 13—16, determine whether the...Ch. 3.3 - In Exercises 13—16, determine whether the...Ch. 3.3 - A popu1aon has mean =7 and standard deviation =2....Ch. 3.3 - A population has mean =25 and standard deviation...Ch. 3.3 - In Exercises 19 and 20, identify the outlier. Then...Ch. 3.3 - Prob. 16ECh. 3.3 - For the data set 37 82 20 25 31 10 41 44 4 36 68...Ch. 3.3 - For the data set Find the first and third...Ch. 3.3 - For the data set Find the 58th percentile. Find...Ch. 3.3 - For the data set Find the 80th percentile. Find...Ch. 3.3 - Prob. 21ECh. 3.3 - A fish story: The mean length of one-year-old...Ch. 3.3 - Blood pressure in men: The three quartiles for...Ch. 3.3 - Blood pressure in women: The article referred to...Ch. 3.3 - Hazardous waste: Following is a list of the number...Ch. 3.3 - Cholesterol levels: The National Health and...Ch. 3.3 - Commuting to work: Jamie drives to work every...Ch. 3.3 - Windy city by the bay: Following are wind speeds...Ch. 3.3 - Caffeine: Following are the number of grams of...Ch. 3.3 - Prob. 30ECh. 3.3 - Prob. 31ECh. 3.3 - Prob. 32ECh. 3.3 - Bragging rights: After learning his score on a...Ch. 3.3 - Who scored the highest? On a final exam in a large...Ch. 3.3 - Prob. 35ECh. 3.3 - Prob. 36ECh. 3.3 - Prob. 37ECh. 3.3 - Prob. 38ECh. 3.3 - Prob. 39ECh. 3.3 - Boxplot possible? 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