Statistical Reasoning for Everyday Life - MyStatLab
5th Edition
ISBN: 9781323823781
Author: Bennett
Publisher: PEARSON
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Chapter 1.1, Problem 1E
To determine
State any two different meanings of the term “statistics”.
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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 1 Solutions
Statistical Reasoning for Everyday Life - MyStatLab
Ch. 1.1 - Prob. 1ECh. 1.1 - Basic Definitions. Define the terms population,...Ch. 1.1 - Confidence Interval. What is a margin of error,...Ch. 1.1 - Statistical Process. Describe the five basic steps...Ch. 1.1 - Does It Make Sense? For Exercises 510, determine...Ch. 1.1 - Does It Make Sense? For Exercises 510, determine...Ch. 1.1 - Does It Make Sense? For Exercises 510, determine...Ch. 1.1 - Does It Make Sense? For Exercises 510, determine...Ch. 1.1 - Does It Make Sense? For Exercises 510, determine...Ch. 1.1 - Does It Make Sense? For Exercises 510, determine...
Ch. 1.1 - Prob. 11ECh. 1.1 - Population, Sample, Statistic, and Parameter....Ch. 1.1 - Population, Sample, Statistic, and Parameter....Ch. 1.1 - Population, Sample, Statistic, and Parameter....Ch. 1.1 - Identifying the Confidence Interval. In Exercises...Ch. 1.1 - Identifying the Confidence Interval. In Exercises...Ch. 1.1 - Identifying the Confidence Interval. In Exercises...Ch. 1.1 - Identifying the Confidence Interval. In Exercises...Ch. 1.1 - Identifying the Confidence Interval. In Exercises...Ch. 1.1 - Identifying the Confidence Interval. In Exercises...Ch. 1.1 - Forming Conclusions. For each of Exercises 2124,...Ch. 1.1 - Forming Conclusions. For each of Exercises 2124,...Ch. 1.1 - Forming Conclusions. For each of Exercises 2124,...Ch. 1.1 - Forming Conclusions. For each of Exercises 2124,...Ch. 1.1 - Interpreting Real Studies. For each of Exercises...Ch. 1.1 - Interpreting Real Studies. For each of Exercises...Ch. 1.1 - Interpreting Real Studies. For each of Exercises...Ch. 1.1 - Interpreting Real Studies. For each of Exercises...Ch. 1.1 - Five Steps in a Study. Describe how you would...Ch. 1.1 - Five Steps in a Study. Describe how you would...Ch. 1.1 - Five Steps in a Study. Describe how you would...Ch. 1.1 - Five Steps in a Study. Describe how you would...Ch. 1.2 - Census and Sample. What is a census, what is a...Ch. 1.2 - Representative Sample. What is a representative...Ch. 1.2 - Biased Sample. What is a biased sample, and what...Ch. 1.2 - Sampling Methods. List and define five common...Ch. 1.2 - Does It Make Sense? For Exercises 58, determine...Ch. 1.2 - Does It Make Sense? For Exercises 58, determine...Ch. 1.2 - Does It Make Sense? For Exercises 58, determine...Ch. 1.2 - Does It Make Sense? For Exercises 58, determine...Ch. 1.2 - Census. In Exercises 912, determine whether a...Ch. 1.2 - Census. In Exercises 912, determine whether a...Ch. 1.2 - Census. In Exercises 912, determine whether a...Ch. 1.2 - Census. In Exercises 912, determine whether a...Ch. 1.2 - Representative Samples? In Exercises 1316,...Ch. 1.2 - Representative Samples? In Exercises 1316,...Ch. 1.2 - Representative Samples? In Exercises 1316,...Ch. 1.2 - Representative Samples? In Exercises 1316,...Ch. 1.2 - Evaluate the Sample Choices. Exercises 17 and 18...Ch. 1.2 - Evaluate the Sample Choices. Exercises 17 and 18...Ch. 1.2 - Bias. In Exercises 1922, determine whether there...Ch. 1.2 - Bias. In Exercises 1922, determine whether there...Ch. 1.2 - Bias. In Exercises 1922, determine whether there...Ch. 1.2 - Bias. In Exercises 1922, determine whether there...Ch. 1.2 - Sampling Methods. In Exercises 2338, identify...Ch. 1.2 - Sampling Methods. In Exercises 2338, identify...Ch. 1.2 - Sampling Methods. In Exercises 2338, identify...Ch. 1.2 - Sampling Methods. In Exercises 2338, identify...Ch. 1.2 - Sampling Methods. In Exercises 2338, identify...Ch. 1.2 - Sampling Methods. In Exercises 2338, identify...Ch. 1.2 - Sampling Methods. In Exercises 2338, identify...Ch. 1.2 - Sampling Methods. In Exercises 2338, identify...Ch. 1.2 - Sampling Methods. In Exercises 2338, identify...Ch. 1.2 - Sampling Methods. In Exercises 2338, identify...Ch. 1.2 - Sampling Methods. In Exercises 2338, identify...Ch. 1.2 - Sampling Methods. In Exercises 2338, identify...Ch. 1.2 - Sampling Methods. In Exercises 2338, identify...Ch. 1.2 - Sampling Methods. In Exercises 2338, identify...Ch. 1.2 - Sampling Methods. In Exercises 2338, identify...Ch. 1.2 - Sampling Methods. In Exercises 2338, identify...Ch. 1.2 - Choosing Sampling Methods. For each of Exercises...Ch. 1.2 - Prob. 40ECh. 1.2 - Prob. 41ECh. 1.2 - Choosing Sampling Methods. For each of Exercises...Ch. 1.3 - Variables. Define variable, variables, of...Ch. 1.3 - Confounding. In testing the effectiveness of a new...Ch. 1.3 - Placebo. What is a placebo, and why is it...Ch. 1.3 - Blinding. What is blinding, and why is it...Ch. 1.3 - Does It Make Sense? For Exercises 58, determine...Ch. 1.3 - Does It Make Sense? For Exercises 58, determine...Ch. 1.3 - Does It Make Sense? For Exercises 58, determine...Ch. 1.3 - Does It Make Sense? For Exercises 58, determine...Ch. 1.3 - Type of Study. For Exercises 920, determine...Ch. 1.3 - Type of Study. For Exercises 920, determine...Ch. 1.3 - Type of Study. For Exercises 920, determine...Ch. 1.3 - Type of Study. For Exercises 920, determine...Ch. 1.3 - Type of Study. For Exercises 920, determine...Ch. 1.3 - Type of Study. For Exercises 920, determine...Ch. 1.3 - Type of Study. For Exercises 920, determine...Ch. 1.3 - Type of Study. For Exercises 920, determine...Ch. 1.3 - Type of Study. For Exercises 920, determine...Ch. 1.3 - Type of Study. For Exercises 920, determine...Ch. 1.3 - Type of Study. For Exercises 920, determine...Ch. 1.3 - Type of Study. For Exercises 920, determine...Ch. 1.3 - Confounding. For each of the studies described in...Ch. 1.3 - Confounding. For each of the studies described in...Ch. 1.3 - Confounding. For each of the studies described in...Ch. 1.3 - Confounding. For each of the studies described in...Ch. 1.3 - Confounding. For each of the studies described in...Ch. 1.3 - Confounding. For each of the studies described in...Ch. 1.3 - Confounding. For each of the studies described in...Ch. 1.3 - Confounding. For each of the studies described in...Ch. 1.3 - Analyzing Experiments. Exercises 2932 present...Ch. 1.3 - Analyzing Experiments. Exercises 2932 present...Ch. 1.3 - Analyzing Experiments. Exercises 2932 present...Ch. 1.3 - Analyzing Experiments. Exercises 2932 present...Ch. 1.4 - Critical Evaluation. Briefly describe the eight...Ch. 1.4 - Peer Review. What is peer review? How is it...Ch. 1.4 - Selection Bias and Participation Bias. Describe...Ch. 1.4 - Self-Selected Surveys. Why are self-selected...Ch. 1.4 - Does It Make Sense? For Exercises 58, determine...Ch. 1.4 - Does It Make Sense? For Exercises 58, determine...Ch. 1.4 - Does It Make Sense? For Exercises 58, determine...Ch. 1.4 - Does It Make Sense? For Exercises 58, determine...Ch. 1.4 - Applying Guidelines. In Exercises 916, determine...Ch. 1.4 - Applying Guidelines. In Exercises 916, determine...Ch. 1.4 - Applying Guidelines. In Exercises 916, determine...Ch. 1.4 - Applying Guidelines. In Exercises 916, determine...Ch. 1.4 - Applying Guidelines. In Exercises 916, determine...Ch. 1.4 - Applying Guidelines. In Exercises 916, determine...Ch. 1.4 - Applying Guidelines. In Exercises 916, determine...Ch. 1.4 - Applying Guidelines. In Exercises 916, determine...Ch. 1.4 - Bias. In each of Exercises 1720, identify and...Ch. 1.4 - Bias. In each of Exercises 1720, identify and...Ch. 1.4 - Bias. In each of Exercises 1720, identify and...Ch. 1.4 - Bias. In each of Exercises 1720, identify and...Ch. 1.4 - Its All in the Wording. Princeton Survey Research...Ch. 1.4 - Tax or Spend? A Gallup poll asked the following...Ch. 1.4 - Accurate Headlines? Exercises 23 and 24 give a...Ch. 1.4 - Accurate Headlines? Exercises 23 and 24 give a...Ch. 1.4 - Stat Bites. Politicians commonly believe that they...Ch. 1.4 - Stat Bites. Politicians commonly believe that they...Ch. 1.4 - Stat Bites. Politicians commonly believe that they...Ch. 1.4 - Stat Bites. Politicians commonly believe that they...Ch. 1 - Medication Usage In a survey of 3005 adults aged...Ch. 1 - Simple Random Sample. An important element of this...Ch. 1 - Echinacea Treatment. Rhinoviruses typically cause...Ch. 1 - Wording of a Survey Question. In The...Ch. 1 - In Exercises 15, assume that you conduct a survey...Ch. 1 - In Exercises 15, assume that you conduct a survey...Ch. 1 - In Exercises 15, assume that you conduct a survey...Ch. 1 - In Exercises 15, assume that you conduct a survey...Ch. 1 - In Exercises 15, assume that you conduct a survey...Ch. 1 - In Exercises 610, consider a clinical trial...Ch. 1 - In Exercises 610, consider a clinical trial...Ch. 1 - In Exercises 610, consider a clinical trial...Ch. 1 - In Exercises 610, consider a clinical trial...Ch. 1 - In Exercises 610, consider a clinical trial...Ch. 1 - In a Marist Poll, respondents chose the most...Ch. 1 - From the poll results given in Exercise 11, can we...Ch. 1 - Consider a study in which you measure the weights...Ch. 1 - Consider a survey of randomly selected people in...Ch. 1 - If a statistical study is carefully conducted in...Ch. 1 - Public Health Is Your Lifestyle Healthy? Consider...Ch. 1 - Prob. 2.3FCh. 1 - Prob. 2.5F
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