Introductory Statistics Plus Mylab Statistics With Pearson Etext -- Access Card Package (3rd Edition)
3rd Edition
ISBN: 9780135229996
Author: Robert Gould, Rebecca Wong, Colleen N. Ryan
Publisher: PEARSON
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Textbook Question
Chapter 5, Problem 14SE
Guessing on Tests Consider a multiple-choice test with a total of four possible options for each question.
a. What is the
b. What is the probability that a guess on one question will be incorrect?
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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 5 Solutions
Introductory Statistics Plus Mylab Statistics With Pearson Etext -- Access Card Package (3rd Edition)
Ch. 5 - Simulation (Example 1) If we flip a coin 10 times,...Ch. 5 - Simulation Suppose you are carrying out a...Ch. 5 - Empirical versus Theoretical A Monopoly player...Ch. 5 - Empirical versus Theoretical A person was trying...Ch. 5 - Empirical versus Theoretical A student flips a...Ch. 5 - Empirical versus Theoretical A bag of candy...Ch. 5 - Medical Group A medical practice group consists of...Ch. 5 - Teacher Effectiveness A recent study found that...Ch. 5 - Probability For each of the values, state whether...Ch. 5 - Probability For each of the values, state whether...
Ch. 5 - Cards (Example 2) There are four suits: clubs ,...Ch. 5 - Playing Cards Refer to exercise 5.11 for...Ch. 5 - Guessing on Tests a. On a true/false quiz in which...Ch. 5 - Guessing on Tests Consider a multiple-choice test...Ch. 5 - Four Coin Tosses (Example 3) The sample space...Ch. 5 - Three Children The sample space shows all possible...Ch. 5 - Birthdays What is the probability that a baby will...Ch. 5 - Playing Cards If one card is selected from a...Ch. 5 - Vacations (Example 4) The Gallup poll asked...Ch. 5 - Reading The Pew Research Center asked a sample of...Ch. 5 - Marijuana Legalization (Example 5) A Gallup poll...Ch. 5 - Marijuana Legalization Use the data in exercise...Ch. 5 - Gender Discrimination in Tech (Example 6) A Pew...Ch. 5 - Gender Discrimination in Tech Use the data in...Ch. 5 - Mutually Exclusive Suppose a person is selected at...Ch. 5 - Mutually Exclusive Suppose a student is selected...Ch. 5 - Vacations (Mutually Exclusive) (Example 7)...Ch. 5 - Vacations (Not Mutually Exclusive) Refer to the...Ch. 5 - Fair Die (Example 8) Roll a fair six-sided die. a....Ch. 5 - Fair Die Roll a fair six-sided die. a. What is the...Ch. 5 - Grades Assume that the only grades possible in a...Ch. 5 - Changing Multiple-Choice Answers One of the...Ch. 5 - Commuting A college conducted a student survey to...Ch. 5 - Political Parties Political science researchers...Ch. 5 - Super Powers (Example 9) A 2018 Marist poll asked...Ch. 5 - Online Presence A 2018 Pew poll asked U.S. adults...Ch. 5 - Thumbtacks When a certain type of thumbtack is...Ch. 5 - Thumbtacks When a certain type of thumbtack is...Ch. 5 - Multiple-Choice Exam An exam consists of 12...Ch. 5 - Driving Exam A driving exam consists of 30...Ch. 5 - Equal Rights for Women (Example 10) A recent Pew...Ch. 5 - Equal Rights for Women A person is selected...Ch. 5 - Frequent Stress (Example 11) A Gallup poll asked...Ch. 5 - Frequent Stress Use the data in exercise 5.43 for...Ch. 5 - Independent? Suppose a person is chosen at random....Ch. 5 - Independent? About 12#37; of men and 10#37; of...Ch. 5 - Independent? Suppose a person is chosen at random....Ch. 5 - Independent? Ring sizes typically range from about...Ch. 5 - Equal Rights Poll (Example 12) Refer to the table...Ch. 5 - Equal Rights Poll Assume a person is selected...Ch. 5 - Hand Folding (Example 13) When people fold their...Ch. 5 - Dice When two dice are rolled, is the event “the...Ch. 5 - TV News Source and Gender (Example 14) A 2018 Pew...Ch. 5 - TV News Source and Gender Using the table in...Ch. 5 - Coin (Example 15) Imagine flipping three fair...Ch. 5 - Die Imagine rolling a fair six-sided die three...Ch. 5 - Die Sequences (Example 16) Roll a fair six-sided...Ch. 5 - Babies Assume that babies born are equally likely...Ch. 5 - Vacations (Example 17) According to a recent...Ch. 5 - Landlines and Cell Phones According to the...Ch. 5 - Cervical Cancer (Example 18) According to a study...Ch. 5 - Cervical Cancer About 8 women in 100,000 have...Ch. 5 - Rolling Sixes (Example 19) What’s the probability...Ch. 5 - Rolling a Sum of 7 What’s the probability of...Ch. 5 - Multiple-Choice Test (Example 20) A...Ch. 5 - True/False Test A true/false test has 20...Ch. 5 - Simulating Coin Flips (Example 21) a. Use the line...Ch. 5 - Simulating Rolling a Die a. Explain how you could...Ch. 5 - Law of Large Numbers Refer to Histograms A, B, and...Ch. 5 - Law of Large Numbers The table shows the results...Ch. 5 - Coin Flips Imagine flipping a fair coin many...Ch. 5 - Coin Flips, Again Refer to the following figure....Ch. 5 - Law of Large Numbers: Gambling Betty and Jane are...Ch. 5 - LLN: Grandchildren Consider two pairs of...Ch. 5 - LLN: Coin If you flip a fair coin repeatedly and...Ch. 5 - LLN: Die The graph shows the average when a...Ch. 5 - Jury Duty A jury is supposed to represent the...Ch. 5 - Left-handed Some estimates say that 10#37; of the...Ch. 5 - Simulation: Four-Sided Die a. Explain how you...Ch. 5 - Simulation: Six-Sided Die a. Explain how you could...Ch. 5 - Prob. 81CRECh. 5 - Prob. 82CRECh. 5 - Independent Variables Use your general knowledge...Ch. 5 - Independent Variables Use your general knowledge...Ch. 5 - Prob. 85CRECh. 5 - Prob. 86CRECh. 5 - Prob. 87CRECh. 5 - Prob. 88CRECh. 5 - Birthdays Suppose all the days of the week are...Ch. 5 - Pass Rate of Written Driver’s Exam In California,...Ch. 5 - Prob. 91CRECh. 5 - Reading Habits In 2016 the Pew Research Center...Ch. 5 - Prob. 93CRECh. 5 - Prob. 94CRECh. 5 - Prob. 95CRECh. 5 - Cell Phone Security A 2017 Pew Research poll found...Ch. 5 - Coin Flips Let H stand for heads and let T stand...Ch. 5 - Prob. 98CRECh. 5 - Prob. 99CRECh. 5 - Online Dating The Pew Research Center asked a...Ch. 5 - CA Bar Exam In order to practice law, lawyers must...Ch. 5 - Driving Tests In addition to behind-the-wheel...Ch. 5 - California Recidivism and Gender Women return to...Ch. 5 - Blue Eyes About 17#37; of American men have blue...Ch. 5 - Prob. 105CRECh. 5 - Prob. 106CRECh. 5 - Law of Large Numbers A famous study by Amos...Ch. 5 - Law of Large Numbers A certain professional...Ch. 5 - Climate Change and Political Party In 2016 a Pew...Ch. 5 - Climate Change and Political Party Refer to the...Ch. 5 - Prob. 111CRECh. 5 - Prob. 112CRECh. 5 - Prob. 113CRECh. 5 - Prob. 114CRECh. 5 - Prob. 115CRECh. 5 - Prob. 116CRECh. 5 - Prob. 117CRECh. 5 - Prob. 118CRECh. 5 - Prob. 119CRECh. 5 - Prob. 120CRECh. 5 - Prob. 121CRECh. 5 - Multiple-Choice Test A multiple-choice test has 10...Ch. 5 - Simulating Guessing on a Multiple-Choice Test...Ch. 5 - Simulating Guessing on a True/False Test Perform a...Ch. 5 - Red Light/Green Light A busy street has three...Ch. 5 - Soda A soda-bottling plant has a flaw in that...
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