Developmental Mathematics (9th Edition)
Developmental Mathematics (9th Edition)
9th Edition
ISBN: 9780321997173
Author: Marvin L. Bittinger, Judith A. Beecher
Publisher: PEARSON
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Chapter I, Problem 33ES
To determine

To calculate: The midpoint of the segment with the endpoints (2, 1) and (3, 4).

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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.)
3. Consider the polynomial equation 6-iz+7z² - iz³ +z = 0 for which the roots are 3i, -2i, -i, and i. (a) Verify the relations between this roots and the coefficients of the polynomial. (b) Find the annulus region in which the roots lie.
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…
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