EBK MATHEMATICS WITH APPLICATIONS IN TH
12th Edition
ISBN: 9780134773285
Author: MULLINS
Publisher: YUZU
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Chapter 10, Problem 45RE
To determine
To graph: The five-number summary box-plot for the sales in May 2016.
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most 2, and let
Let P2 denote the vector space of polynomials of degree at
D: P2➡ P2
be the transformation that sends a polynomial p(t) = at² + bt+c in P2 to its derivative
p'(t)
2at+b, that is,
D(p) = p'.
(a) Prove that D is a linear transformation.
(b) Find a basis for the kernel ker(D) of the linear transformation D and compute its
nullity.
(c) Find a basis for the image im(D) of the linear transformation D and compute its
rank.
(d) Verify that the Rank-Nullity Theorem holds for the linear transformation D.
(e) Find the matrix representation of D in the standard basis (1,t, t2) of P2.
The Mason group has a liability of £200,000 to be paid in 14 years' time. It wants to Redington immunise these liabilities with assets consisting of amount P in
a bank and Q 18-year zero coupon bonds, with P and Q to be determined. Interest is compounded monthly at rate 8%.
(a)
Answer:
What is the present value of the liability? Enter your answer correct to the nearest pound.
(b) What is the duration of the liability? Enter your answer correct to 3 significant digits.
Answer:
(c) What is the convexity of the liability? Enter your answer correct to 3 significant digits.
Answer:
(d)
Write down the two equations that P and Q need to satisfy for Redington immunisation to hold and solve these equations for P and Q. Enter the
answers correct to the nearest pound.
Answers: P=
Q=
(e) What is the convexity of the assets in this case? Enter your answer correct to 3 significant digits.
Answer:
(f)
Is the convexity condition that is necessary for Redington immunisation satisfied in this case?…
Dr Fogg is quoted the following market prices VT for T-year unit zero-coupon bonds
as well as the fair forward rate
V3 = 0.95 and V9 = 0.7
f3.5 = 4%.
(a) Determine the spot rate $3. Enter your answer as a percentage correct to 3 significant digits.
Answer:
(b)
Answer:
(c)
Answer:
(d)
Determine the spot rate s9. Enter your answer as a percentage correct to 3 significant digits.
Find the fair forward rate f3,9. Enter your answer as a percentage correct to 3 significant digits.
Dr Fogg wants to sign a forward contract to buy 20kg of tea in 5 years' time. The current price of tea is £2.7 per kg. Find the fair forward price of
this contract. Enter your answer correct to the nearest penny.
Answer:
Chapter 10 Solutions
EBK MATHEMATICS WITH APPLICATIONS IN TH
Ch. 10.1 - Checkpoint 1 A restaurant trade group commissioned...Ch. 10.1 - Checkpoint 2
Make a histogram and a frequency...Ch. 10.1 - Checkpoint 3
Make a stem-and-leaf plot for the...Ch. 10.1 - Checkpoint 4
List the original data for the...Ch. 10.1 - Checkpoint 5
Characterize the shape of the...Ch. 10.1 - SP 500 Stocks The data for Exercises 1 -4 consist...Ch. 10.1 - SP 500 Stocks The data for Exercises 1 -4 consist...Ch. 10.1 - SP 500 Stocks The data for Exercises 1 -4 consist...Ch. 10.1 - SP 500 Stocks The data for Exercises 1 -4 consist...Ch. 10.1 - The data for Exercises 5-10 consist of random...
Ch. 10.1 - The data for Exercises 5-10 consist of random...Ch. 10.1 - The data for Exercises 5-10 consist of random...Ch. 10.1 - The data for Exercises 5-10 consist of random...Ch. 10.1 - The data for Exercises 5-10 consist of random...Ch. 10.1 - The data for Exercises 5-10 consist of random...Ch. 10.1 - For Exercises 11-20, construct a stem-and-leaf...Ch. 10.1 - For Exercises 11-20, construct a stem-and-leaf...Ch. 10.1 - For Exercises 11-20, construct a stem-and-leaf...Ch. 10.1 - Prob. 14ECh. 10.1 - For Exercises 11-20, construct a stem-and-leaf...Ch. 10.1 - For Exercises 11-20, construct a stem-and-leaf...Ch. 10.1 - Prob. 17ECh. 10.1 - Prob. 18ECh. 10.1 - For Exercises 11-20, construct a stem-and-leaf...Ch. 10.1 - For Exercises 11-20, construct a stem-and-leaf...Ch. 10.1 - Describe the shape of each of the given...Ch. 10.1 - Describe the shape of each of the given...Ch. 10.1 - Describe the shape of each of the given...Ch. 10.1 - Describe the shape of each of the given...Ch. 10.1 - Student Loan Defaults The following histogram...Ch. 10.1 - Stocks The following histogram shows the stock...Ch. 10.1 - Cat Ownership The stem-and-leaf plot below...Ch. 10.1 - Personal Bankruptcies The stem-and-leaf plot below...Ch. 10.1 - 29. Test Scores The grade distribution for scores...Ch. 10.1 - 30. Test Scores The grade distribution for scores...Ch. 10.2 - Checkpoint 1
Find the mean dollar amount of the...Ch. 10.2 - Checkpoint 2
Find for the following frequency...Ch. 10.2 - Checkpoint 3
Find the mean of the following...Ch. 10.2 - Checkpoint 4
Find the mean for the college tuition...Ch. 10.2 - Checkpoint 5
Find the median for the given heights...Ch. 10.2 - Checkpoint 6
Find the mode for each of the given...Ch. 10.2 - Checkpoint 7
Following is a list of the number of...Ch. 10.2 - Prob. 8CPCh. 10.2 - Prob. 1ECh. 10.2 - Prob. 2ECh. 10.2 - Prob. 3ECh. 10.2 - Prob. 4ECh. 10.2 - Prob. 5ECh. 10.2 - Prob. 6ECh. 10.2 - Prob. 7ECh. 10.2 - Prob. 8ECh. 10.2 - Prob. 9ECh. 10.2 - Prob. 10ECh. 10.2 - Prob. 11ECh. 10.2 - Prob. 12ECh. 10.2 - Prob. 13ECh. 10.2 - Prob. 14ECh. 10.2 - Find the mode or modes for each of the given lists...Ch. 10.2 - Find the mode or modes for each of the given lists...Ch. 10.2 - Find the mode or modes for each of the given lists...Ch. 10.2 - Find the mode or modes for each of the given lists...Ch. 10.2 - Find the mode or modes for each of the given lists...Ch. 10.2 - 20. When is the median the most appropriate...Ch. 10.2 - 21. When would the mode be an appropriate measure...Ch. 10.2 - Pet Ownership For Exercises 22 and 23, the...Ch. 10.2 - Pet Ownership For Exercises 22 and 23, the...Ch. 10.2 - 24. To predict the outcome of the next...Ch. 10.2 - Work each problem. (See Example 6.) MLB Payrolls...Ch. 10.2 - Work each problem. (See Example 6.) NFL Team...Ch. 10.2 - Work each problem. (See Example 6.)
27. Business...Ch. 10.2 - Work each problem. (See Example 6.) Sirius XM...Ch. 10.2 - Work each problem. (See Example 6.) Dr Pepper and...Ch. 10.2 - Natural Science The table gives the average...Ch. 10.2 - Natural Science The table gives the average...Ch. 10.2 - For Exercises 32-33 determine the shape of the...Ch. 10.2 - For Exercises 32-33 determine the shape of the...Ch. 10.2 - Prob. 34ECh. 10.2 - Prob. 35ECh. 10.2 - For Exercises 36-38, calculate the weighted...Ch. 10.2 - For Exercises 36-38, calculate the weighted...Ch. 10.2 - For Exercises 36-38, calculate the weighted...Ch. 10.2 - Prob. 39ECh. 10.2 - For Exercises 36-38, calculate the weighted...Ch. 10.3 - Checkpoint 1
Find the range for this sample of the...Ch. 10.3 - Checkpoint 2
Find the deviations from the mean for...Ch. 10.3 - Checkpoint 3
Find the standard deviation for a...Ch. 10.3 - Prob. 4CPCh. 10.3 - Prob. 1ECh. 10.3 - Prob. 2ECh. 10.3 - Prob. 3ECh. 10.3 - Prob. 4ECh. 10.3 - Prob. 5ECh. 10.3 - Prob. 6ECh. 10.3 - Prob. 7ECh. 10.3 - Finance Use the following table for Exercises...Ch. 10.3 - Finance Use the following table for Exercises...Ch. 10.3 - Prob. 10ECh. 10.3 - Education Find the standard deviation for the...Ch. 10.3 - Prob. 12ECh. 10.3 - Prob. 13ECh. 10.3 - Prob. 14ECh. 10.3 - Prob. 15ECh. 10.3 - Prob. 16ECh. 10.3 - Prob. 17ECh. 10.3 - Prob. 18ECh. 10.3 - Prob. 19ECh. 10.3 - Prob. 20ECh. 10.3 - Prob. 21ECh. 10.3 - Prob. 22ECh. 10.3 - Prob. 23ECh. 10.3 - Movie Studios' Revenue For Exercises 23-28, use...Ch. 10.3 - Prob. 25ECh. 10.3 - Prob. 26ECh. 10.3 - Prob. 27ECh. 10.3 - Prob. 28ECh. 10.3 - Prob. 29ECh. 10.3 - Prob. 30ECh. 10.3 - Prob. 34ECh. 10.3 - Prob. 31ECh. 10.3 - Prob. 32ECh. 10.3 - Prob. 33ECh. 10.3 - IBM and Microsoft Revenue The following table...Ch. 10.3 - Prob. 36ECh. 10.3 - Prob. 37ECh. 10.3 - Prob. 38ECh. 10.3 - IBM and Microsoft Revenue The following table...Ch. 10.3 - Prob. 40ECh. 10.3 - Prob. 41ECh. 10.3 - Prob. 42ECh. 10.3 - Prob. 43ECh. 10.3 - Prob. 44ECh. 10.3 - Prob. 45ECh. 10.3 - Prob. 46ECh. 10.3 - Prob. 47ECh. 10.3 - Prob. 48ECh. 10.4 - Prob. 1CPCh. 10.4 - Prob. 2CPCh. 10.4 - Prob. 3CPCh. 10.4 - Prob. 4CPCh. 10.4 - Prob. 5CPCh. 10.4 - Prob. 6CPCh. 10.4 - Prob. 7CPCh. 10.4 - 1. The peak in a normal curve occurs directly...Ch. 10.4 - Prob. 2ECh. 10.4 - Prob. 3ECh. 10.4 - Prob. 4ECh. 10.4 - Prob. 5ECh. 10.4 - Prob. 6ECh. 10.4 - Prob. 7ECh. 10.4 - Prob. 8ECh. 10.4 - Find the percentage of the total area under the...Ch. 10.4 - Prob. 10ECh. 10.4 - Prob. 11ECh. 10.4 - Prob. 12ECh. 10.4 - Prob. 13ECh. 10.4 - Prob. 14ECh. 10.4 - Prob. 15ECh. 10.4 - Prob. 16ECh. 10.4 - Prob. 17ECh. 10.4 - Prob. 18ECh. 10.4 - Prob. 19ECh. 10.4 - 20. Using Chebyshev’s theorem and the normal...Ch. 10.4 - Prob. 21ECh. 10.4 - Prob. 22ECh. 10.4 - Prob. 23ECh. 10.4 - Prob. 24ECh. 10.4 - Prob. 25ECh. 10.4 - Prob. 26ECh. 10.4 - Prob. 27ECh. 10.4 - Prob. 28ECh. 10.4 - Prob. 29ECh. 10.4 - Prob. 30ECh. 10.4 - Prob. 31ECh. 10.4 - Prob. 32ECh. 10.4 - Prob. 33ECh. 10.4 - Prob. 34ECh. 10.4 - Prob. 35ECh. 10.4 - Prob. 36ECh. 10.4 - Prob. 37ECh. 10.4 - Prob. 38ECh. 10.4 - Prob. 39ECh. 10.4 - Prob. 40ECh. 10.4 - Prob. 41ECh. 10.4 - Prob. 42ECh. 10.4 - Prob. 43ECh. 10.4 - Prob. 44ECh. 10.4 - Prob. 45ECh. 10.4 - Prob. 46ECh. 10.4 - Prob. 47ECh. 10.4 - Prob. 48ECh. 10.4 - Prob. 49ECh. 10.4 - Education The mean performance score of a large...Ch. 10.4 - Prob. 51ECh. 10.4 - Prob. 52ECh. 10.4 - Job Satisfaction According to a 2016 study...Ch. 10.4 - Prob. 54ECh. 10.4 - Prob. 55ECh. 10.4 - Prob. 56ECh. 10.4 - Prob. 57ECh. 10.4 - Prob. 58ECh. 10.4 - Student Loan Debt According to a report from the...Ch. 10.4 - Prob. 60ECh. 10.4 - Prob. 61ECh. 10.4 - Prob. 62ECh. 10 - NASDAQ 100 Stocks For Exercises 1-10, the data...Ch. 10 - Prob. 2RECh. 10 - Prob. 3RECh. 10 - Prob. 4RECh. 10 - Prob. 5RECh. 10 - Prob. 6RECh. 10 - NASDAQ 100 Stocks For Exercises 1-10, the data...Ch. 10 - Prob. 8RECh. 10 - Prob. 9RECh. 10 - Prob. 10RECh. 10 - Prob. 11RECh. 10 - Prob. 12RECh. 10 - Prob. 13RECh. 10 - Prob. 14RECh. 10 - Prob. 15RECh. 10 - Prob. 16RECh. 10 - Prob. 17RECh. 10 - Prob. 18RECh. 10 - Prob. 19RECh. 10 - Prob. 20RECh. 10 - Prob. 21RECh. 10 - Prob. 22RECh. 10 - Prob. 23RECh. 10 - Prob. 24RECh. 10 - Find the standard deviation for each of the given...Ch. 10 - Prob. 26RECh. 10 - Prob. 27RECh. 10 - Prob. 28RECh. 10 - Prob. 29RECh. 10 - Prob. 30RECh. 10 - Prob. 31RECh. 10 - Prob. 32RECh. 10 - Prob. 33RECh. 10 - Prob. 34RECh. 10 - Prob. 35RECh. 10 - Prob. 36RECh. 10 - Arm Circumference Data from a recent National...Ch. 10 - Prob. 38RECh. 10 - Prob. 39RECh. 10 - Prob. 40RECh. 10 - Prob. 41RECh. 10 - Prob. 42RECh. 10 - Prob. 43RECh. 10 - Prob. 44RECh. 10 - Prob. 45RECh. 10 - Prob. 46RECh. 10 - Prob. 47RECh. 10 - College or University Education A recent...Ch. 10 - College or University Education A recent...Ch. 10 - Prob. 50RECh. 10 - Prob. 51RECh. 10 - Prob. 52RECh. 10 - Prob. 53RECh. 10 - Prob. 54RECh. 10 - Prob. 1CECh. 10 - Prob. 2CECh. 10 - Prob. 3CECh. 10 - Prob. 4CECh. 10 - Prob. 5CECh. 10 - Prob. 6CECh. 10 - Prob. 7CECh. 10 - Prob. 8CECh. 10 - Prob. 9CECh. 10 - Prob. 10CE
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- (c) Let A = -1 3 -4 12 3 3 -9 (i) Find bases for row(A), col(A) and N(A). (ii) Determine the rank and nullity of A, and verify that the Rank-Nullity Theorem holds for the above matrix A.arrow_forwardSuppose that the price S(t) in year t of stocks of Bancroft & Sons is modelled by a stochastic process which has a risk-neutral distribution at time t = 3 given by £120 with probability 0.3, S(3): = £140 with probability 0.5, £160 with probability 0.2. Assume that interest is compounded continuously at nominal rate 2%. (a) Assuming no-arbitrage, determine the current price S(0) of Bancroft & Sons stock. Enter your answer correct to the nearest pound. Answer: (b) Determine the no-arbitrage price of a European put option on Bancroft & Sons stock with strike 150 and expiry 3 years. Enter your answer correct to the nearest pound. Answer:arrow_forwardA 2-year bond with face value £300,000 is redeemable at half-par and has semi-annual coupons paid at annual rate 4%. Suppose that interest is compounded quarterly at nominal rate 3%. (a) Answer: What is the amount of the first payment? (b) What is the amount of the last payment? Answer: (c) Determine the no-arbitrage price of the bond. Enter your answer correct to the nearest pound. Answer: (d) Determine the duration of the cash flow generated by the bond. Enter your answer correct to 3 significant digits. Answer:arrow_forward
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