Mathematical Statistics with Applications
7th Edition
ISBN: 9780495110811
Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer
Publisher: Cengage Learning
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Chapter 9.2, Problem 7E
To determine
Derive the efficiency of
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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.)
The managing director of a consulting group has the accompanying monthly data on total overhead costs and professional labor hours to bill to clients. Complete parts a through c.
Question content area bottom
Part 1
a. Develop a simple linear regression model between billable hours and overhead costs.
Overhead
Costsequals=212495.2212495.2plus+left parenthesis 42.4857 right parenthesis42.485742.4857times×Billable
Hours
(Round the constant to one decimal place as needed. Round the coefficient to four decimal places as needed. Do not include the $ symbol in your answers.)
Part 2
b. Interpret the coefficients of your regression model. Specifically, what does the fixed component of the model mean to the consulting firm?
Interpret the fixed term,
b 0b0,
if appropriate. Choose the correct answer below.
A.
The value of
b 0b0
is the predicted billable hours for an overhead cost of 0 dollars.
B.
It is not appropriate to interpret
b 0b0,
because its value…
Using the accompanying Home Market Value data and associated regression line,
Market ValueMarket Valueequals=$28,416+$37.066×Square
Feet, compute the errors associated with each observation using the formula
e Subscript ieiequals=Upper Y Subscript iYiminus−ModifyingAbove Upper Y with caret Subscript iYi
and construct a frequency distribution and histogram.
LOADING...
Click the icon to view the Home Market Value data.
Question content area bottom
Part 1
Construct a frequency distribution of the errors,
e Subscript iei.
(Type whole numbers.)
Error
Frequency
minus−15 comma 00015,000less than<
e Subscript iei
less than or equals≤minus−10 comma 00010,000
0
minus−10 comma 00010,000less than<
e Subscript iei
less than or equals≤minus−50005000
5
minus−50005000less than<
e Subscript iei
less than or equals≤0
21
0less than<
e Subscript iei
less than or equals≤50005000
9…
Chapter 9 Solutions
Mathematical Statistics with Applications
Ch. 9.2 - Prob. 1ECh. 9.2 - Let Y1, Y2,, Yn denote a random sample from a...Ch. 9.2 - Let Y1, Y2, , Yn denote a random sample from the...Ch. 9.2 - Let Y1, Y2, , Yn denote a random sample of size n...Ch. 9.2 - Suppose that Y1, Y2, , Yn is a random sample from...Ch. 9.2 - Prob. 6ECh. 9.2 - Prob. 7ECh. 9.2 - Let Y1, Y2, , Yn denote a random sample from a...Ch. 9.3 - Applet Exercise How was Figure 9.1 obtained?...Ch. 9.3 - Applet Exercise Refer to Exercise 9.9. Scroll down...
Ch. 9.3 - Applet Exercise Refer to Exercises 9.9 and 9.10....Ch. 9.3 - Applet Exercise Refer to Exercise 9.11. What...Ch. 9.3 - Applet Exercise Refer to Exercises 9.99.12. Access...Ch. 9.3 - Applet Exercise Refer to Exercise 9.13. Scroll...Ch. 9.3 - Refer to Exercise 9.3. Show that both 1 and 2 are...Ch. 9.3 - Refer to Exercise 9.5. Is 22 a consistent...Ch. 9.3 - Suppose that X1, X2,, Xn and Y1, Y2,,Yn are...Ch. 9.3 - In Exercise 9.17, suppose that the populations are...Ch. 9.3 - Let Y1, Y2,,Yn denote a random sample from the...Ch. 9.3 - If Y has a binomial distribution with n trials and...Ch. 9.3 - Let Y1, Y2,, Yn be a random sample of size n from...Ch. 9.3 - Refer to Exercise 9.21. Suppose that Y1, Y2,, Yn...Ch. 9.3 - Refer to Exercise 9.21. Suppose that Y1, Y2,, Yn...Ch. 9.3 - Let Y1, Y2, Y3, Yn be independent standard normal...Ch. 9.3 - Suppose that Y1, Y2, , Yn denote a random sample...Ch. 9.3 - Prob. 26ECh. 9.3 - Use the method described in Exercise 9.26 to show...Ch. 9.3 - Let Y1, Y2, , Yn denote a random sample of size n...Ch. 9.3 - Let Y1, Y2, , Yn denote a random sample of size n...Ch. 9.3 - Let Y1, Y2, , Yn be independent random variables,...Ch. 9.3 - Prob. 31ECh. 9.3 - Let Y1, Y2, , Yn denote a random sample from the...Ch. 9.3 - An experimenter wishes to compare the numbers of...Ch. 9.3 - Prob. 34ECh. 9.3 - Let Y1, Y2, be a sequence of random variables with...Ch. 9.3 - Suppose that Y has a binomial distribution based...Ch. 9.4 - Prob. 37ECh. 9.4 - Let Y1, Y2, , Yn denote a random sample from a...Ch. 9.4 - Let Y1, Y2, , Yn denote a random sample from a...Ch. 9.4 - Prob. 40ECh. 9.4 - Let Y1, Y2, , Yn denote a random sample from a...Ch. 9.4 - If Y1, Y2, , Yn denote a random sample from a...Ch. 9.4 - Prob. 43ECh. 9.4 - Let Y1, Y2, , Yn denote independent and...Ch. 9.4 - Suppose that Y1, Y2, , Yn is a random sample from...Ch. 9.4 - If Y1, Y2,, Yn denote a random sample from an...Ch. 9.4 - Refer to Exercise 9.43. If is known, show that...Ch. 9.4 - Refer to Exercise 9.44. If is known, show that...Ch. 9.4 - Let Y1, Y2, . . . , Yn denote a random sample from...Ch. 9.4 - Let Y1, Y2, . . . , Yn denote a random sample from...Ch. 9.4 - Prob. 51ECh. 9.4 - Prob. 52ECh. 9.4 - Prob. 53ECh. 9.4 - Prob. 54ECh. 9.4 - Let Y1, Y2, . . . , Yn denote independent and...Ch. 9.5 - Refer to Exercise 9.38(b). Find an MVUE of 2. 9.38...Ch. 9.5 - Refer to Exercise 9.18. Is the estimator of 2...Ch. 9.5 - Refer to Exercise 9.40. Use i=1nYi2 to find an...Ch. 9.5 - The number of breakdowns Y per day for a certain...Ch. 9.5 - Prob. 60ECh. 9.5 - Refer to Exercise 9.49. Use Y(n) to find an MVUE...Ch. 9.5 - Refer to Exercise 9.51. Find a function of Y(1)...Ch. 9.5 - Prob. 63ECh. 9.5 - Let Y1, Y2, , Yn be a random sample from a normal...Ch. 9.5 - In this exercise, we illustrate the direct use of...Ch. 9.5 - The likelihood function L(y1,y2,,yn|) takes on...Ch. 9.5 - Refer to Exercise 9.66. Suppose that a sample of...Ch. 9.5 - Prob. 68ECh. 9.6 - Prob. 69ECh. 9.6 - Suppose that Y1, Y2, , Yn constitute a random...Ch. 9.6 - If Y1, Y2, , Yn denote a random sample from the...Ch. 9.6 - If Y1, Y2, , Yn denote a random sample from the...Ch. 9.6 - An urn contains black balls and N white balls....Ch. 9.6 - Let Y1, Y2,, Yn constitute a random sample from...Ch. 9.6 - Prob. 75ECh. 9.6 - Let X1, X2, X3, be independent Bernoulli random...Ch. 9.6 - Let Y1, Y2,, Yn denote independent and identically...Ch. 9.6 - Let Y1, Y2,, Yn denote independent and identically...Ch. 9.6 - Let Y1, Y2,, Yn denote independent and identically...Ch. 9.7 - Suppose that Y1, Y2,, Yn denote a random sample...Ch. 9.7 - Suppose that Y1, Y2, , Yn denote a random sample...Ch. 9.7 - Prob. 82ECh. 9.7 - Suppose that Y1, Y2, , Yn constitute a random...Ch. 9.7 - Prob. 84ECh. 9.7 - Let Y1, Y2,, Yn denote a random sample from the...Ch. 9.7 - Suppose that X1, X2, , Xm, representing yields per...Ch. 9.7 - A random sample of 100 voters selected from a...Ch. 9.7 - Prob. 88ECh. 9.7 - It is known that the probability p of tossing...Ch. 9.7 - A random sample of 100 men produced a total of 25...Ch. 9.7 - Find the MLE of based on a random sample of size...Ch. 9.7 - Prob. 92ECh. 9.7 - Prob. 93ECh. 9.7 - Suppose that is the MLE for a parameter . Let t()...Ch. 9.7 - A random sample of n items is selected from the...Ch. 9.7 - Consider a random sample of size n from a normal...Ch. 9.7 - The geometric probability mass function is given...Ch. 9.8 - Refer to Exercise 9.97. What is the approximate...Ch. 9.8 - Consider the distribution discussed in Example...Ch. 9.8 - Suppose that Y1, Y2, . . . , Yn constitute a...Ch. 9.8 - Let Y1, Y2, . . . , Yn denote a random sample of...Ch. 9.8 - Refer to Exercises 9.97 and 9.98. If a sample of...Ch. 9 - Prob. 103SECh. 9 - Prob. 104SECh. 9 - Refer to Exercise 9.38(b). Under the conditions...Ch. 9 - Prob. 106SECh. 9 - Suppose that a random sample of length-of-life...Ch. 9 - The MLE obtained in Exercise 9.107 is a function...Ch. 9 - Prob. 109SECh. 9 - Refer to Exercise 9.109. a Find the MLE N2 of N. b...Ch. 9 - Refer to Exercise 9.110. Suppose that enemy tanks...Ch. 9 - Let Y1, Y2, . . . , Yn denote a random sample from...
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