
Introductory Statistics
1st Edition
ISBN: 9781938168208
Author: Barbara Illowsky, Susan Dean
Publisher: OpenStax College
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Textbook Question
Chapter 1, Problem 10P
The population is ________
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Does there appear to be a positive or negative relationship between price and screen size? Use a scatter plot to examine the relationship. How to take snapshots: if you use a MacBook, press Command+ Shift+4 to take snapshots. If you are using Windows, use the Snipping Tool to take snapshots.
Question 1: Determine and interpret the correlation coefficient between the two variables. In your interpretation, discuss the direction of the relationship (positive, negative, or zero relationship). Also discuss the strength of the relationship.
Value of correlation coefficient:
Direction of the relationship (positive, negative, or zero relationship):
Strength of the relationship (strong/moderate/weak):
Question 2: Estimate the relationship between screen size and price using a simple linear regression model and interpret the estimated coefficients. In your interpretation, tell the dollar amount by which price will change for each unit of increase in screen size. (The answer for the…
In this problem, we consider a Brownian motion (W+) t≥0. We consider a stock model (St)t>0
given (under the measure P) by
d.St 0.03 St dt + 0.2 St dwt,
with So 2. We assume that the interest rate is r = 0.06. The purpose of this problem is to
price an option on this stock (which we name cubic put). This option is European-type, with
maturity 3 months (i.e. T = 0.25 years), and payoff given by
F = (8-5)+
(a) Write the Stochastic Differential Equation satisfied by (St) under the risk-neutral measure
Q. (You don't need to prove it, simply give the answer.)
(b) Give the price of a regular European put on (St) with maturity 3 months and strike K = 2.
(c) Let X =
S. Find the Stochastic Differential Equation satisfied by the process (Xt)
under the measure Q.
(d) Find an explicit expression for X₁ = S3 under measure Q.
(e) Using the results above, find the price of the cubic put option mentioned above.
(f) Is the price in (e) the same as in question (b)? (Explain why.)
Problem 4. Margrabe formula and the Greeks (20 pts)
In the homework, we determined the Margrabe formula for the price of an option allowing you to
swap an x-stock for a y-stock at time T. For stocks with initial values xo, yo, common volatility
σ and correlation p, the formula was given by
Fo=yo (d+)-x0Þ(d_),
where
In (±²
Ꭲ
d+
õ√T
and
σ = σ√√√2(1 - p).
дго
(a) We want to determine a "Greek" for ỡ on the option: find a formula for
θα
(b) Is
дго
θα
positive or negative?
(c) We consider a situation in which the correlation p between the two stocks increases: what
can you say about the price Fo?
(d) Assume that yo< xo and p = 1. What is the price of the option?
Chapter 1 Solutions
Introductory Statistics
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Nominal,...Ch. 1 - Design an experiment. Identify the explanatory and...Ch. 1 - Discuss potential violations of the rule requiring...Ch. 1 - For each of the following eight exercises,...Ch. 1 - For each of the following eight exercises,...Ch. 1 - For each of the following eight exercises,...Ch. 1 - For each of the following eight exercises,...Ch. 1 - For each of the following eight exercises,...Ch. 1 - For each of the following eight exercises,...Ch. 1 - For each of the following eight exercises,...Ch. 1 - For each of the following eight exercises,...Ch. 1 - Use the following information to answer the next...Ch. 1 - Use the following information to answer the next...Ch. 1 - Use the following information to answer the next...Ch. 1 - For the following exercises, identify (he type of...Ch. 1 - For the following exercises, identify (he type of...Ch. 1 - For the following exercises, identify (he type of...Ch. 1 - For the following exercises, identify (he type of...Ch. 1 - For the following exercises, identify (he type of...Ch. 1 - For the following exercises, identify (he type of...Ch. 1 - For the following exercises, identify (he type of...Ch. 1 - For the following exercises, identify (he type of...Ch. 1 - For the following exercises, identify (he type of...Ch. 1 - For the following exercises, identify (he type of...Ch. 1 - Use the following information to answer the next...Ch. 1 - Use the following information to answer the next...Ch. 1 - Airline companies are interested in the...Ch. 1 - Suppose you want to determine the mean number of...Ch. 1 - Suppose you want to determine the mean number of...Ch. 1 - List some practical difficulties involved in...Ch. 1 - List some practical difficulties involved in...Ch. 1 - With your classmates, brainstorm some ways you...Ch. 1 - The instructor takes her sample by gathering data...Ch. 1 - A study was done to determine the age, number of...Ch. 1 - Name the sampling method used in each of the...Ch. 1 - A “random survey” was conducted of 3,2’4 people of...Ch. 1 - The Well-Being Index is a survey that follows...Ch. 1 - In advance of the 1936 Presidential Election, a...Ch. 1 - Crime-related and demographic statistics for 4 US...Ch. 1 - YouPolls is a website that allows anyone to create...Ch. 1 - A scholarly article about response rates begins...Ch. 1 - Fifty part-time students were asked how many...Ch. 1 - Sixty adults with gum disease were asked the...Ch. 1 - Nineteen immigrants to the U.S were asked how many...Ch. 1 - How much time does it take to navel to work? Table...Ch. 1 - Forbes magazine published data on the best small...Ch. 1 - Use (he following information o answer the next...Ch. 1 - Use (he following information o answer the next...Ch. 1 - How does sleep deprivation affect your ability to...Ch. 1 - An advertisement for Acme Investments displays the...Ch. 1 - The graph in Figure 1.15 shows the number of...Ch. 1 - Seven hundred and Seventy-one distance learning...Ch. 1 - Several online textbook retailers advertise that...
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