Discrete Mathematics
5th Edition
ISBN: 9780134689562
Author: Dossey, John A.
Publisher: Pearson,
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Chapter 2.1, Problem 26E
To determine
The condition under which the equation
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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…
Chapter 2 Solutions
Discrete Mathematics
Ch. 2.1 - Prob. 1ECh. 2.1 - Prob. 2ECh. 2.1 - Prob. 3ECh. 2.1 - Prob. 4ECh. 2.1 - In Exercises 5–8, compute A × B for each of the...Ch. 2.1 - In Exercises 5–8, compute A × B for each of the...Ch. 2.1 - In Exercises 5–8, compute A × B for each of the...Ch. 2.1 - Prob. 8ECh. 2.1 - Prob. 9ECh. 2.1 - Prob. 10E
Ch. 2.1 - Prob. 11ECh. 2.1 - Prob. 12ECh. 2.1 - Give an example of sets for which , but A ≠ B.
Ch. 2.1 - Give an example of sets for which , but A ≠ B.
Ch. 2.1 - Give an example of sets for which , but A ≠ B.
Ch. 2.1 - Give an example of sets for which (A − B) − C ≠ A...Ch. 2.1 - Use Theorems 2.1 and 2.2 as in Example 2.4 to...Ch. 2.1 - Use Theorems 2.1 and 2.2 as in Example 2.4 to...Ch. 2.1 - Use Theorems 2.1 and 2.2 as in Example 2.4 to...Ch. 2.1 - Prob. 20ECh. 2.1 - Prob. 21ECh. 2.1 - Prob. 22ECh. 2.1 - Prob. 23ECh. 2.1 - Use Theorems 2.1 and 2.2 as in Example 2.4 to...Ch. 2.1 - If A is a set containing m elements and B is a set...Ch. 2.1 - Under what conditions is A − B = B − A?
Ch. 2.1 - Under what conditions is A ⋃ B = A?
Ch. 2.1 - Under what conditions is A ⋂ B = A?
Ch. 2.1 - Prob. 29ECh. 2.1 - Prob. 30ECh. 2.1 - Prob. 31ECh. 2.1 - Prob. 32ECh. 2.1 - Prob. 33ECh. 2.1 - Prob. 34ECh. 2.1 - Prob. 35ECh. 2.1 - Prob. 36ECh. 2.1 - Prob. 37ECh. 2.1 - Prove the set equalities in Exercises...Ch. 2.1 - Prob. 39ECh. 2.1 - Prove that (A × C) ⋃ (B × D) ⊆ (A ⋃ B) × (C ⋃ D).
Ch. 2.2 - In Exercises 1–12, determine which of the...Ch. 2.2 - In Exercises 1–12, determine which of the...Ch. 2.2 - In Exercises 1–12, determine which of the...Ch. 2.2 - In Exercises 1–12, determine which of the...Ch. 2.2 - In Exercises 1-12, determine which of the...Ch. 2.2 - Prob. 6ECh. 2.2 - In Exercises 1–12, determine which of the...Ch. 2.2 - Prob. 8ECh. 2.2 - In Exercises 1–12, determine which of the...Ch. 2.2 - In Exercises 1–12, determine which of the...Ch. 2.2 - In Exercises 1–12, determine which of the...Ch. 2.2 - Prob. 12ECh. 2.2 - In Exercises 13-18, show that the given relation R...Ch. 2.2 - In Exercises 13-18, show that the given relation R...Ch. 2.2 - In Exercises 13-18, show that the given relation R...Ch. 2.2 - In Exercises 13-18, show that the given relation R...Ch. 2.2 - Prob. 17ECh. 2.2 - In Exercises 13–18, show that the given relation R...Ch. 2.2 - Prob. 19ECh. 2.2 - Write the equivalence relation on {1, 2, 3, 4, 5,...Ch. 2.2 - Prob. 21ECh. 2.2 - Prob. 22ECh. 2.2 - Prob. 23ECh. 2.2 - Let R1 and R2 be equivalence relations on sets S1...Ch. 2.2 - Determine the number of relations on a set S...Ch. 2.2 - Prob. 26ECh. 2.2 - Prob. 27ECh. 2.2 - How many partitions are there of a set containing...Ch. 2.2 - Prob. 29ECh. 2.2 - Prob. 30ECh. 2.2 - Prob. 31ECh. 2.2 - Prob. 33ECh. 2.3 - In Exercises 1–8, determine whether the given...Ch. 2.3 - Prob. 2ECh. 2.3 - Prob. 3ECh. 2.3 - Prob. 4ECh. 2.3 - Prob. 5ECh. 2.3 - Prob. 6ECh. 2.3 - Prob. 7ECh. 2.3 - Prob. 8ECh. 2.3 - Prob. 9ECh. 2.3 - Prob. 10ECh. 2.3 - Prob. 11ECh. 2.3 - Prob. 12ECh. 2.3 - Prob. 13ECh. 2.3 - Prob. 14ECh. 2.3 - Prob. 15ECh. 2.3 - Prob. 16ECh. 2.3 - Prob. 17ECh. 2.3 - Prob. 18ECh. 2.3 - Prob. 19ECh. 2.3 - Prob. 20ECh. 2.3 - Prob. 21ECh. 2.3 - Prob. 22ECh. 2.3 - Prob. 23ECh. 2.3 - Prob. 24ECh. 2.3 - Prob. 25ECh. 2.3 - Prob. 26ECh. 2.3 - Prob. 27ECh. 2.3 - Consider the “divides” relation on the set of...Ch. 2.3 - Prob. 29ECh. 2.3 - Prob. 30ECh. 2.3 - Prob. 31ECh. 2.3 - Prob. 32ECh. 2.3 - Prob. 33ECh. 2.3 - Prob. 34ECh. 2.3 - Prob. 35ECh. 2.3 - Prob. 37ECh. 2.3 - Prob. 38ECh. 2.3 - Prob. 39ECh. 2.3 - Prob. 40ECh. 2.3 - Prob. 41ECh. 2.3 - Prob. 42ECh. 2.4 - In Exercises 1–4, determine which of the given...Ch. 2.4 - In Exercises 1–4, determine which of the given...Ch. 2.4 - In Exercises 1–4, determine which of the given...Ch. 2.4 - In Exercises 1–4, determine which of the given...Ch. 2.4 - In Exercises 5–12, determine whether the given g...Ch. 2.4 - In Exercises 5–12, determine whether the given g...Ch. 2.4 - In Exercises 5–12, determine whether the given g...Ch. 2.4 - In Exercises 5–12, determine whether the given g...Ch. 2.4 - In Exercises 5–12, determine whether the given g...Ch. 2.4 - In Exercises 5–12, determine whether the given g...Ch. 2.4 - In Exercises 5–12, determine whether the given g...Ch. 2.4 - In Exercises 5–12, determine whether the given g...Ch. 2.4 - Prob. 13ECh. 2.4 - Prob. 14ECh. 2.4 - Prob. 15ECh. 2.4 - Prob. 16ECh. 2.4 - Prob. 17ECh. 2.4 - Prob. 18ECh. 2.4 - Prob. 19ECh. 2.4 - Prob. 20ECh. 2.4 - Prob. 21ECh. 2.4 - Prob. 22ECh. 2.4 - Prob. 23ECh. 2.4 - Prob. 24ECh. 2.4 - Prob. 25ECh. 2.4 - Prob. 26ECh. 2.4 - Prob. 27ECh. 2.4 - Prob. 28ECh. 2.4 - Prob. 29ECh. 2.4 - Prob. 30ECh. 2.4 - Prob. 31ECh. 2.4 - Prob. 32ECh. 2.4 - Prob. 33ECh. 2.4 - Prob. 34ECh. 2.4 - Prob. 35ECh. 2.4 - Prob. 36ECh. 2.4 - Prob. 37ECh. 2.4 - Prob. 38ECh. 2.4 - Prob. 39ECh. 2.4 - Determine formulas for the functions gf and fg in...Ch. 2.4 - Prob. 41ECh. 2.4 - Prob. 42ECh. 2.4 - Prob. 43ECh. 2.4 - Prob. 44ECh. 2.4 - In Exercises 45–52, Z denotes the set of integers....Ch. 2.4 - In Exercises 45–52, Z denotes the set of integers....Ch. 2.4 - In Exercises 45–52, Z denotes the set of integers....Ch. 2.4 - In Exercises 45–52, Z denotes the set of integers....Ch. 2.4 - Prob. 49ECh. 2.4 - In Exercises 45–52, Z denotes the set of integers....Ch. 2.4 - In Exercises 45–52, Z denotes the set of integers....Ch. 2.4 - Prob. 52ECh. 2.4 - In Exercises 53–60, X denotes the set of real...Ch. 2.4 - In Exercises 53–60, X denotes the set of real...Ch. 2.4 - In Exercises 53–60, X denotes the set of real...Ch. 2.4 - In Exercises 53–60, X denotes the set of real...Ch. 2.4 - In Exercises 53–60, X denotes the set of real...Ch. 2.4 - In Exercises 53–60, X denotes the set of real...Ch. 2.4 - In Exercises 53–60, X denotes the set of real...Ch. 2.4 - In Exercises 53–60, X denotes the set of real...Ch. 2.4 - Find a subset Y of the set of real numbers X such...Ch. 2.4 - Find a subset Y of the set of real numbers X such...Ch. 2.4 - Prob. 63ECh. 2.4 - If X has m elements and Y has n elements, how many...Ch. 2.4 - Prob. 65ECh. 2.4 - Prob. 66ECh. 2.4 - Prob. 67ECh. 2.4 - Prob. 68ECh. 2.4 - Prob. 69ECh. 2.4 - Prob. 70ECh. 2.5 - Compute the Fibonacci numbers F1 through F10.
Ch. 2.5 - Suppose that a number xn is defined recursively by...Ch. 2.5 - Prob. 3ECh. 2.5 - Prob. 4ECh. 2.5 - Prob. 5ECh. 2.5 - Prob. 6ECh. 2.5 - Prob. 7ECh. 2.5 - Prob. 8ECh. 2.5 - Prob. 9ECh. 2.5 - In Exercises 7–10, determine what is wrong with...Ch. 2.5 - In Exercises 11–26, prove each of the given...Ch. 2.5 - In Exercises 11–26, prove each of the given...Ch. 2.5 - Prob. 13ECh. 2.5 - Prob. 14ECh. 2.5 - Prob. 15ECh. 2.5 - Prob. 16ECh. 2.5 - Prob. 17ECh. 2.5 - In Exercises 11–26, prove each of the given...Ch. 2.5 - Prob. 19ECh. 2.5 - Prob. 20ECh. 2.5 - Prob. 21ECh. 2.5 - Prob. 22ECh. 2.5 - Prob. 23ECh. 2.5 - Prob. 24ECh. 2.5 - Prob. 25ECh. 2.5 - Prob. 26ECh. 2.5 - A sequence s0, s1, s2,… is called a geometric...Ch. 2.5 - A sequence, s0, s1, s2,… is called an arithmetic...Ch. 2.6 - Prob. 1ECh. 2.6 - Prob. 2ECh. 2.6 - Prob. 3ECh. 2.6 - Evaluate the numbers in Exercises 1–12.
4. C(12,...Ch. 2.6 - Evaluate the numbers in Exercises 1–12.
5. C(11,...Ch. 2.6 - Prob. 6ECh. 2.6 - Prob. 7ECh. 2.6 - Evaluate the numbers in Exercises 1–12.
8. C(13,...Ch. 2.6 - Evaluate the numbers in Exercises 1–12.
9. C(n,...Ch. 2.6 - Prob. 10ECh. 2.6 - Prob. 11ECh. 2.6 - Evaluate the numbers in Exercises 1–12.
12.
Ch. 2.6 - Prob. 13ECh. 2.6 - How many nonempty subsets of the set {a, e, i, o,...Ch. 2.6 - At Avanti’s, a pizza can be ordered with any...Ch. 2.6 - If a test consists of 12 questions to be answered...Ch. 2.6 - Prob. 17ECh. 2.6 - Jennifer’s grandmother has told her that she can...Ch. 2.6 - Prob. 19ECh. 2.6 - Prob. 20ECh. 2.6 - Prob. 21ECh. 2.6 - Prob. 22ECh. 2.6 - Prob. 23ECh. 2.6 - Prob. 24ECh. 2.6 - Prob. 25ECh. 2.6 - Prob. 26ECh. 2.6 - Prob. 27ECh. 2.6 - Prob. 28ECh. 2.6 - Prove each of the statements in Exercises 29–40 by...Ch. 2.6 - Prob. 30ECh. 2.6 - Prob. 31ECh. 2.6 - Prove each of the statements in Exercises 29–40 by...Ch. 2.6 - Prob. 33ECh. 2.6 - Prove each of the statements in Exercises 29–40 by...Ch. 2.6 - Prob. 35ECh. 2.6 - Prob. 36ECh. 2 - Prob. 1SECh. 2 - Prob. 2SECh. 2 - Prob. 3SECh. 2 - Prob. 4SECh. 2 - Prob. 5SECh. 2 - Prob. 6SECh. 2 - Prob. 7SECh. 2 - Prob. 8SECh. 2 - Prob. 9SECh. 2 - Draw Venn diagrams depicting the sets in Exercises...Ch. 2 - Prob. 11SECh. 2 - Prob. 12SECh. 2 - Prob. 13SECh. 2 - Prob. 14SECh. 2 - Prob. 15SECh. 2 - Prob. 16SECh. 2 - Prob. 17SECh. 2 - Prob. 18SECh. 2 - Prob. 19SECh. 2 - Prob. 20SECh. 2 - Prob. 21SECh. 2 - Prob. 22SECh. 2 - Prob. 23SECh. 2 - Prob. 24SECh. 2 - Prob. 25SECh. 2 - Prob. 26SECh. 2 - Prob. 27SECh. 2 - Prob. 28SECh. 2 - Prob. 29SECh. 2 - Prob. 30SECh. 2 - Prob. 31SECh. 2 - Prob. 32SECh. 2 - Prob. 33SECh. 2 - Prob. 34SECh. 2 - Prob. 35SECh. 2 - How many equivalence relations on S = {a, b, c}...Ch. 2 - Prob. 37SECh. 2 - Prob. 38SECh. 2 - Prob. 39SECh. 2 - Prob. 40SECh. 2 - Prob. 41SECh. 2 - Prob. 42SECh. 2 - Prob. 43SECh. 2 - Prob. 44SECh. 2 - Prob. 45SECh. 2 - Prob. 46SECh. 2 - Prob. 47SECh. 2 - Prob. 49SECh. 2 - Prob. 50SECh. 2 - Prob. 51SECh. 2 - Prob. 52SECh. 2 - Prob. 53SECh. 2 - Prob. 54SECh. 2 - Prob. 55SECh. 2 - Prob. 56SECh. 2 - Prob. 57SECh. 2 - Prob. 58SECh. 2 - Prob. 59SECh. 2 - Prob. 60SECh. 2 - Prob. 61SECh. 2 - Prob. 62SECh. 2 - Prob. 63SECh. 2 - Prob. 64SECh. 2 - Prove the results in Exercises 63–72 by...Ch. 2 - Prob. 66SECh. 2 - Prob. 67SECh. 2 - Prob. 68SECh. 2 - Prob. 69SECh. 2 - Prob. 70SECh. 2 - Prob. 71SECh. 2 - Prob. 72SECh. 2 - Prob. 1CPCh. 2 - Prob. 6CPCh. 2 - Prob. 7CPCh. 2 - Prob. 12CP
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- 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.arrow_forwardWrite the equation of the trigonometric function shown in the graph. LO 5 4 3 2 1 y -5 -5 4 8 8 500 -1 -2 -3 -4 -5 x 5 15л 5л 25л 15л 35π 5л 4 8 2 8 4 8arrow_forwardc) Using only Laplace transforms solve the following Samuelson model given below i.e., the second order difference equation (where yt is national income): - Yt+2 6yt+1+5y₁ = 0, if y₁ = 0 for t < 0, and y₁ = 0, y₁ = 1 1-e-s You may use without proof that L-1[s(1-re-s)] = f(t) = r² for n ≤tarrow_forward5. 156 m/WXY = 59° 63 E 7. B E 101 C mFE = 6. 68° 8. C 17arrow_forwardScoring: MATH 15 FILING /10 COMPARISON /10 RULER I 13 Express EMPLOYMENT PROFESSIONALS NAME: SKILLS EVALUATION TEST- Light Industrial MATH-Solve the following problems. (Feel free to use a calculator.) DATE: 1. If you were asked to load 225 boxes onto a truck, and the boxes are crated, with each crate containing nine boxes, how many crates would you need to load? 2. Imagine you live only one mile from work and you decide to walk. If you walk four miles per hour, how long will it take you to walk one mile? 3. Add 3 feet 6 inches + 8 feet 2 inches + 4 inches + 2 feet 5 inches. 4. In a grocery store, steak costs $3.85 per pound. If you buy a three-pound steak and pay for it with a $20 bill, how much change will you get? 5. Add 8 minutes 32 seconds + 37 minutes 18 seconds + 15 seconds. FILING - In the space provided, write the number of the file cabinet where the company should be filed. Example: File Cabinet #4 Elson Co. File Cabinets: 1. Aa-Bb 3. Cg-Dz 5. Ga-Hz 7. La-Md 9. Na-Oz 2. Bc-Cf…arrow_forwardpart 3 of the question is: A power outage occurs 6 min after the ride started. Passengers must wait for their cage to be manually cranked into the lowest position in order to exit the ride. Sine function model: where h is the height of the last passenger above the ground measured in feet and t is the time of operation of the ride in minutes. What is the height of the last passenger at the moment of the power outage? Verify your answer by evaluating the sine function model. Will the last passenger to board the ride need to wait in order to exit the ride? Explain.arrow_forwardIf you were asked to load 225 boxes onto a truck, and the boxes are crated, with each crate containing nine boxes, how many crates would you need to load?arrow_forwardForce with 800 N and 400 N are acting on a machine part at 30° and 60°, respectively with the positive x axisarrow_forward2. The duration of the ride is 15 min. (a) How many times does the last passenger who boarded the ride make a complete loop on the Ferris wheel? (b) What is the position of that passenger when the ride ends?arrow_forwardFind the accumulated amount A, if the principal P is invested at an interest rate of r per year for t years. (Round your answer to the nearest cent.) P = $13,000, r = 6%, t = 10, compounded quarterly A = $ 31902 Need Help? Read It Watch It Viewing Saved Work Revert to Last Response SUBMIT ANSWER O/6.66 Points] DETAILS MY NOTES TANAPCALC10 5.3.003. EVIOUS ANSWERS ASK YOUR TEACHER PRACTICE ANOTHER Find the accumulated amount A, if the principal P is invested at an interest rate of r per year for t years. (Round your answer to the nearest cent.) P = $140,000, r = 8%, t = 8, compounded monthly A = $259130.20 X Need Help? Read It Watch Itarrow_forwardFind the present value of $20,000 due in 3 years at the given rate of interest. (Round your answers to the nearest cent.) (a) 2%/year compounded monthly (b) 5%/year compounded daily $ Need Help? Read It Watch It SUBMIT ANSWER [-/6.66 Points] DETAILS MY NOTES TANAPCALC10 5.3.009. ASK YOUR TEACHER PRACTICE ANC Find the accumulated amount after 3 years if $4000 is invested at 3%/year compounded continuously. (Round your answer to the nearest cent.) Need Help? Read It Watch Itarrow_forwardFind the effective rate corresponding to the given nominal rate. (Round your answers to three decimal places.) (a) 9.5%/year compounded monthly % (b) 9.5%/year compounded daily % Need Help? Read It Watch It SUBMIT ANSWER -/6.66 Points] DETAILS MY NOTES TANAPCALC10 5.3.007. ASK YOUR TEACHE Find the present value of $90,000 due in 7 years at the given rate of interest. (Round your answers to the nearest cent.) (a) 9%/year compounded semiannually (b) 9%/year compounded quarterly LAarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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