Introduction to Statistics and Data Analysis
5th Edition
ISBN: 9781305115347
Author: Roxy Peck; Chris Olsen; Jay L. Devore
Publisher: Brooks Cole
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Textbook Question
Chapter 2.3, Problem 45E
The paper “Turning to Learn: Screen Orientation and Reasoning from Small Devices” (Computers in Human Behavior [2011]: 793-797) describes a study that investigated whether cell phones with small screens are useful for gathering information. The researchers wondered if the ability to reason using information read on a small screen was affected by the screen orientation. The researchers assigned 33 undergraduate students who were enrolled in a psychology course at a large public university to one of two groups at random.
One group read material that was displayed on a small screen in portrait orientation, and the other group read material on the same size screen but turned to display the information in landscape orientation (see figure below).
The researchers found that performance on a reasoning test that was based on the displayed material was better for the group that read material in the landscape orientation.
- a. Is the desert bed study an observational study or an experiment?
- b. Did the study use random selection from some population?
- c. Did the study use random assignment to expert mental groups?
- d. Is the conclusion—that reasoning using information displayed on a small screen is improved by terming the screen to landscape orientation—appropriate, given the study design? Explain.
- e. Is it reasonable to generalize the conclusions from this study to some larger population? If so, what population?
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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.)
Chapter 2 Solutions
Introduction to Statistics and Data Analysis
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