Introduction to Probability and Statistics
14th Edition
ISBN: 9781133103752
Author: Mendenhall, William
Publisher: Cengage Learning
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Textbook Question
Chapter 8.5, Problem 8.30E
Compare the confidence intervals in Exercise 8.29. What effect does each of these actions have on the width of a confidence interval?
a. Double the
b. Quadruple the sample size
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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 8 Solutions
Introduction to Probability and Statistics
Ch. 8.4 - Prob. 8.3ECh. 8.4 - Prob. 8.4ECh. 8.4 - Prob. 8.5ECh. 8.4 - Prob. 8.6ECh. 8.4 - Prob. 8.7ECh. 8.4 - Prob. 8.8ECh. 8.4 - Prob. 8.9ECh. 8.4 - Prob. 8.10ECh. 8.4 - Prob. 8.11ECh. 8.4 - Prob. 8.12E
Ch. 8.4 - Prob. 8.13ECh. 8.4 - Prob. 8.14ECh. 8.4 - Prob. 8.15ECh. 8.4 - Prob. 8.16ECh. 8.4 - Prob. 8.18ECh. 8.4 - Prob. 8.19ECh. 8.4 - Hotel Costs Even within a particular chain of...Ch. 8.4 - Prob. 8.21ECh. 8.5 - Find and interpret a 95% confidence interval for a...Ch. 8.5 - Find a 90% confidence interval for a population...Ch. 8.5 - Prob. 8.26ECh. 8.5 - Prob. 8.27ECh. 8.5 - Prob. 8.28ECh. 8.5 - Prob. 8.29ECh. 8.5 - Compare the confidence intervals in Exercise 8.29....Ch. 8.5 - Prob. 8.31ECh. 8.5 - Prob. 8.32ECh. 8.5 - Prob. 8.33ECh. 8.5 - Prob. 8.34ECh. 8.5 - Prob. 8.35ECh. 8.5 - Prob. 8.36ECh. 8.5 - Prob. 8.38ECh. 8.5 - What’s Normal? What is normal, when it comes to...Ch. 8.5 - Prob. 8.40ECh. 8.6 - Independent random samples were selected from...Ch. 8.6 - Prob. 8.42ECh. 8.6 - Prob. 8.43ECh. 8.6 - Prob. 8.44ECh. 8.6 - Prob. 8.45ECh. 8.6 - Prob. 8.46ECh. 8.6 - Prob. 8.47ECh. 8.6 - Prob. 8.48ECh. 8.6 - Prob. 8.49ECh. 8.6 - Prob. 8.50ECh. 8.6 - Hotel Costs Refer to Exercise 8.20. The means and...Ch. 8.6 - Noise and Stress To compare the effect of stress...Ch. 8.6 - Prob. 8.53ECh. 8.7 - Prob. 8.54ECh. 8.7 - Prob. 8.55ECh. 8.7 - Prob. 8.56ECh. 8.7 - Prob. 8.58ECh. 8.7 - Prob. 8.61ECh. 8.7 - Prob. 8.64ECh. 8.7 - Prob. 8.65ECh. 8.7 - Prob. 8.66ECh. 8.9 - Prob. 8.67ECh. 8.9 - Prob. 8.68ECh. 8.9 - Prob. 8.69ECh. 8.9 - Prob. 8.70ECh. 8.9 - Prob. 8.71ECh. 8.9 - Prob. 8.72ECh. 8.9 - Prob. 8.73ECh. 8.9 - Prob. 8.75ECh. 8.9 - Prob. 8.77ECh. 8.9 - Prob. 8.78ECh. 8.9 - Prob. 8.80ECh. 8.9 - Prob. 8.81ECh. 8.9 - Prob. 8.83ECh. 8 - Prob. 8.86SECh. 8 - Prob. 8.87SECh. 8 - Prob. 8.88SECh. 8 - Prob. 8.89SECh. 8 - Prob. 8.90SECh. 8 - Prob. 8.91SECh. 8 - Prob. 8.92SECh. 8 - Prob. 8.93SECh. 8 - Prob. 8.94SECh. 8 - Prob. 8.95SECh. 8 - Prob. 8.96SECh. 8 - Prob. 8.98SECh. 8 - Prob. 8.99SECh. 8 - Prob. 8.100SECh. 8 - Prob. 8.101SECh. 8 - Prob. 8.103SECh. 8 - Prob. 8.107SECh. 8 - Prob. 8.108SECh. 8 - Prob. 8.109SECh. 8 - Prob. 8.110SECh. 8 - Prob. 8.111SECh. 8 - Prob. 8.112SECh. 8 - Prob. 8.113SECh. 8 - Prob. 8.114SECh. 8 - Prob. 8.115SECh. 8 - Prob. 8.116SECh. 8 - Prob. 8.117SE
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