EBK THINKING MATHEMATICALLY
6th Edition
ISBN: 8220100802720
Author: Blitzer
Publisher: PEARSON
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Chapter 13.4, Problem 3CVC
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Find the first five non-zero terms of the Taylor series for f(x)
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=
1
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Questions
An insurance company's cumulative incurred claims for the last 5 accident years are given
in the following table:
Development Year
Accident Year 0
2018
1 2 3 4
245 267 274 289 292
2019
255 276 288 294
2020
265 283 292
2021
263 278
2022
271
It can be assumed that claims are fully run off after 4 years. The premiums received for
each year are:
Accident Year Premium
2018
306
2019
312
2020
318
2021
326
2022
330
You do not need to make any allowance for inflation.
1. (a) Calculate the reserve at the end of 2022 using the basic chain ladder method.
(b) Calculate the reserve at the end of 2022 using the Bornhuetter-Ferguson method.
2. Comment on the differences in the reserves produced by the methods in Part 1.
7.
11 m
12.7 m
14 m
S
V=B₁+ B2(h)
9.5 m
16 m
h+s
2
na
62-19 = 37 +, M
h² = Bu-29
Chapter 13 Solutions
EBK THINKING MATHEMATICALLY
Ch. 13.1 - CHECK POINT 1 Four candidates are running for...Ch. 13.1 - CHECK POINT 2 Table 13.2 on page 841 shows the...Ch. 13.1 - Prob. 3CPCh. 13.1 - Prob. 4CPCh. 13.1 - CHECK POINT 5 Table 13.2 on page 841 shows the...Ch. 13.1 - Fill in each blank so that the resulting statement...Ch. 13.1 - Fill in each blank so that the resulting statement...Ch. 13.1 - Fill in each blank so that the resulting statement...Ch. 13.1 - Fill in each blank so that the resulting statement...Ch. 13.1 - Fill in each blank so that the resulting statement...
Ch. 13.1 - Prob. 6CVCCh. 13.1 - Fill in each blank so that the resulting statement...Ch. 13.1 - Prob. 8CVCCh. 13.1 - In Exercises 1-2, the preference ballots for three...Ch. 13.1 - In Exercises 1-2, the preference ballots for three...Ch. 13.1 - In Exercises 3-4, four students are running for...Ch. 13.1 - Prob. 4ECh. 13.1 - Your class is given the option of choosing a day...Ch. 13.1 - Prob. 6ECh. 13.1 - Prob. 7ECh. 13.1 - 8. The travel club members are voting for the...Ch. 13.1 - Four professors are running for chair of the...Ch. 13.1 - Prob. 10ECh. 13.1 - Prob. 11ECh. 13.1 - Use the preference table shown in Exercise 8....Ch. 13.1 - Prob. 13ECh. 13.1 - Use the preference table shown in Exercise 10. Who...Ch. 13.1 - Use the preference table shown in Exercise 7....Ch. 13.1 - Use the preference table shown in Exercise 8....Ch. 13.1 - Use the preference table shown in Exercise 9. Who...Ch. 13.1 - Prob. 18ECh. 13.1 - Prob. 19ECh. 13.1 - Prob. 20ECh. 13.1 - In Exercises 19-22, suppose that the pairwise...Ch. 13.1 - Prob. 22ECh. 13.1 - Prob. 23ECh. 13.1 - Prob. 24ECh. 13.1 - Use the preference table shown in Exercise 9. Who...Ch. 13.1 - Prob. 26ECh. 13.1 - In Exercises 27-30, 72 voters are asked to rank...Ch. 13.1 - Prob. 28ECh. 13.1 - In Exercises 27-30, 72 voters are asked to rank...Ch. 13.1 - In Exercises 27-30, 72 voters are asked to rank...Ch. 13.1 - Prob. 31ECh. 13.1 - Prob. 32ECh. 13.1 - Prob. 33ECh. 13.1 - The programmers at the Theater Channel need to...Ch. 13.1 - 35. Five candidates. A, B, C, D, and E, are...Ch. 13.1 - Prob. 36ECh. 13.1 - Prob. 37ECh. 13.1 - Three candidates, A, B, and C, are running for...Ch. 13.1 - What is a preference ballot?Ch. 13.1 - Prob. 40ECh. 13.1 - Prob. 41ECh. 13.1 - 42. Describe the Borda count method. Is it...Ch. 13.1 - What is the plurality-with-elimination method? Why...Ch. 13.1 - What is the pairwise comparison method? Is it...Ch. 13.1 - Prob. 45ECh. 13.1 - Prob. 46ECh. 13.1 - Prob. 47ECh. 13.1 - Prob. 48ECh. 13.1 - Prob. 49ECh. 13.1 - Make Sense? In Exercises 49-52, determine whether...Ch. 13.1 - Make Sense? In Exercises 49-52, determine whether...Ch. 13.1 - Prob. 52ECh. 13.1 - Prob. 53ECh. 13.1 - In Exercises 53-56, construct a preference table...Ch. 13.1 - Prob. 55ECh. 13.1 - In Exercises 53-56, construct a preference table...Ch. 13.1 - 57. Research and present a group report on how...Ch. 13.1 - Research and present a group report on how voting...Ch. 13.2 - CHECK POINT I The 14 members of the school board...Ch. 13.2 - Prob. 2CPCh. 13.2 - CHECK POINT 3 An election with 120 voters and...Ch. 13.2 - Prob. 4CPCh. 13.2 - Fill in each blank so that the resulting statement...Ch. 13.2 - Fill in each blank so that the resulting statement...Ch. 13.2 - Fill in each blank so that the resulting statement...Ch. 13.2 - Prob. 4CVCCh. 13.2 - Prob. 5CVCCh. 13.2 - Fill in each blank so that the resulting statement...Ch. 13.2 - Voters in a small town are considering four...Ch. 13.2 - 2. Fifty-three people are asked to taste-test and...Ch. 13.2 - Prob. 3ECh. 13.2 - Prob. 4ECh. 13.2 - A town is voting on an ordinance dealing with...Ch. 13.2 - A town is voting on an ordinance dealing with...Ch. 13.2 - 7. The following preference table gives the...Ch. 13.2 - Prob. 8ECh. 13.2 - 9. Members of the Student Activity Committee at a...Ch. 13.2 - Prob. 10ECh. 13.2 - Prob. 11ECh. 13.2 - Prob. 12ECh. 13.2 - In Exercises 11-18, the preference table for an...Ch. 13.2 - Prob. 14ECh. 13.2 - In Exercises 11-18, the preference table for an...Ch. 13.2 - In Exercises 11-18, the preference table for an...Ch. 13.2 - In Exercises 11-18, the preference table for an...Ch. 13.2 - Prob. 18ECh. 13.2 - Prob. 19ECh. 13.2 - Describe the majority criterion.Ch. 13.2 - Describe the head-to-head criterion.Ch. 13.2 - Describe the monotonicity criterion.Ch. 13.2 - 23. Describe the irrelevant alternatives...Ch. 13.2 - 24. In your own words, state Arrow’s Impossibility...Ch. 13.2 - Prob. 25ECh. 13.2 - Is it possible to have election results using a...Ch. 13.2 - Prob. 27ECh. 13.2 - Prob. 28ECh. 13.2 - Make Sense? In Exercises 28-31, determine whether...Ch. 13.2 - Prob. 30ECh. 13.2 - Make Sense? In Exercises 28-31, determine whether...Ch. 13.2 - Prob. 32ECh. 13.2 - Prob. 33ECh. 13.2 - Prob. 34ECh. 13.2 - Prob. 35ECh. 13.2 - Citizen-initiated ballot measures often present...Ch. 13.3 - CHECK POINT 1 The Republic of Amador is composed...Ch. 13.3 - CHECK POINT 2 Refer to Check Point 1 on page 865....Ch. 13.3 - Prob. 3CPCh. 13.3 - Prob. 4CPCh. 13.3 - Prob. 5CPCh. 13.3 - Fill in each blank so that the resulting statement...Ch. 13.3 - Fill in each blank so that the resulting statement...Ch. 13.3 - Fill in each blank so that the resulting statement...Ch. 13.3 - Prob. 4CVCCh. 13.3 - Prob. 5CVCCh. 13.3 - Fill in each blank so that the resulting statement...Ch. 13.3 - Fill in each blank so that the resulting statement...Ch. 13.3 - Throughout this Exercise Set, in computing...Ch. 13.3 - Throughout this Exercise Set, in computing...Ch. 13.3 - Throughout this Exercise Set, in computing...Ch. 13.3 - Throughout this Exercise Set, in computing...Ch. 13.3 - A university is composed of five schools. The...Ch. 13.3 - Prob. 6ECh. 13.3 - 7. A small country is composed of five states. A,...Ch. 13.3 - 8. A small country is comprised of four states, A,...Ch. 13.3 - Prob. 9ECh. 13.3 - Prob. 10ECh. 13.3 - The police department in a large city has 180 new...Ch. 13.3 - Prob. 12ECh. 13.3 - Prob. 13ECh. 13.3 - Prob. 14ECh. 13.3 - 15. Twenty sections of bilingual math courses,...Ch. 13.3 - Prob. 16ECh. 13.3 - A rapid transit service operates 200 buses along...Ch. 13.3 - Refer to Exercise 11. Use Webster’s method to...Ch. 13.3 - A hospital has a nursing staff of 250 nurses...Ch. 13.3 - A hospital has a nursing staff of 250 nurses...Ch. 13.3 - A hospital has a nursing staff of 250 nurses...Ch. 13.3 - A hospital has a nursing staff of 250 nurses...Ch. 13.3 - The table shows the 1790 United States census. In...Ch. 13.3 - Prob. 24ECh. 13.3 - Prob. 25ECh. 13.3 - Prob. 26ECh. 13.3 - 27. Describe how to find a standard divisor.
Ch. 13.3 - 28. Describe how to determine a standard quota for...Ch. 13.3 - Prob. 29ECh. 13.3 - Prob. 30ECh. 13.3 - Describe the apportionment problem.Ch. 13.3 - Prob. 32ECh. 13.3 - Prob. 33ECh. 13.3 - Explain why Hamilton’s method satisfies the quota...Ch. 13.3 - Prob. 35ECh. 13.3 - Suppose that you guess at a modified divisor, d,...Ch. 13.3 - Describe the difference between the modified...Ch. 13.3 - In allocating congressional seats, how does...Ch. 13.3 - 39. How are modified quotas rounded using...Ch. 13.3 - Why might it take longer to guess at a modified...Ch. 13.3 - In this Exercise Set, we have used apportionment...Ch. 13.3 - Prob. 42ECh. 13.3 - Make Sense? In Exercises 42-45, determine whether...Ch. 13.3 - Make Sense? In Exercises 42-45, determine whether...Ch. 13.3 - Prob. 45ECh. 13.3 - Prob. 46ECh. 13.3 - Prob. 47ECh. 13.3 - Prob. 48ECh. 13.3 - A small country is composed of three states, A, B,...Ch. 13.3 - Prob. 50ECh. 13.3 - Research and present a group| report on a brief...Ch. 13.4 - CHECK POINT I Table 13.42 shows the populations of...Ch. 13.4 - CHECK POINT 2 A small country has 100 seats in the...Ch. 13.4 - Prob. 3CPCh. 13.4 - Prob. 1CVCCh. 13.4 - Prob. 2CVCCh. 13.4 - Prob. 3CVCCh. 13.4 - Prob. 4CVCCh. 13.4 - 1. The mathematics department has 30 teaching...Ch. 13.4 - 2. A school district has 57 new laptop computers...Ch. 13.4 - 3. The table shows the populations of three states...Ch. 13.4 - The table at the top of the next column shows the...Ch. 13.4 - A small country has 24 seats in the congress,...Ch. 13.4 - Prob. 6ECh. 13.4 - 7. A town has 40 mail trucks and four districts in...Ch. 13.4 - 8. A town has five districts in which mail is...Ch. 13.4 - A corporation has two branches A and B. Each year...Ch. 13.4 - 10. A corporation has three branches, A, B, and C...Ch. 13.4 - Prob. 11ECh. 13.4 - a. A country has three states, state A, with a...Ch. 13.4 - 13. In Exercise 12, use Jefferson’s method with ...Ch. 13.4 - Prob. 14ECh. 13.4 - Prob. 15ECh. 13.4 - What is the new-states paradox?Ch. 13.4 - 17. According to Balinski and Young’s...Ch. 13.4 - Make Sense? In Exercises 18-21, determine whether...Ch. 13.4 - Prob. 19ECh. 13.4 - Prob. 20ECh. 13.4 - Make Sense? In Exercises 18-21, determine whether...Ch. 13.4 - Give an example of a country with three states in...Ch. 13 - In Exercises 1-8, three candidates, A, B, and C,...Ch. 13 - In Exercises 1-8, three candidates, A, B, and C,...Ch. 13 - In Exercises 1-8, three candidates, A, B, and C,...Ch. 13 - In Exercises 1-8, three candidates, A, B, and C,...Ch. 13 - In Exercises 1–8, three candidates, A, B, and C,...Ch. 13 - In Exercises 1–8, three candidates, A, B, and C,...Ch. 13 - In Exercises 1-8, three candidates, A, B, and C,...Ch. 13 - In Exercises 1-8, three candidates A, B, and C,...Ch. 13 - Use the following preference table to solve...Ch. 13 - Use the following preference table to solve...Ch. 13 - Use the following preference table to solve...Ch. 13 - Prob. 12TCh. 13 - Prob. 13TCh. 13 - Prob. 14TCh. 13 - Prob. 15TCh. 13 - Prob. 16TCh. 13 - In Exercises 16-24, an HMO has 10 doctors to be...Ch. 13 - Prob. 18TCh. 13 - Prob. 19TCh. 13 - Prob. 20TCh. 13 - Prob. 21TCh. 13 - Prob. 22TCh. 13 - Prob. 23TCh. 13 - In Exercises 16-24, an HMO has 10 doctors to be...Ch. 13 - 25. Write one sentence for a person not familiar...Ch. 13 - 1. The 12 preference ballots for four candidates...Ch. 13 - (In Exercises 2-5, be sure to refer to the...Ch. 13 - (In Exercises 2-5, be sure to refer to the...Ch. 13 - (In Exercises 2-5, be sure to refer to the...Ch. 13 - (In Exercises 2-5, be sure to refer to the...Ch. 13 - Prob. 6RECh. 13 - In Exercises 6-9, the Theater Society members are...Ch. 13 - In Exercises 6-9, the Theater Society members are...Ch. 13 - Prob. 9RECh. 13 - Prob. 10RECh. 13 - Prob. 11RECh. 13 - Prob. 12RECh. 13 - In Exercises 10-13, four candidates, A, B, C, and...Ch. 13 - In Exercises 14-16, voters in a small town are...Ch. 13 - In Exercises 14-16, voters in a small town are...Ch. 13 - Prob. 16RECh. 13 - Prob. 17RECh. 13 - Prob. 18RECh. 13 - Prob. 19RECh. 13 - Use the following preference table to solve...Ch. 13 - Prob. 21RECh. 13 - Prob. 22RECh. 13 - Prob. 23RECh. 13 - Prob. 24RECh. 13 - Use the following preference table, which shows...Ch. 13 - Prob. 26RECh. 13 - Prob. 27RECh. 13 - Prob. 28RECh. 13 - Prob. 29RECh. 13 - Prob. 30RECh. 13 - Prob. 31RECh. 13 - Prob. 32RECh. 13 - Prob. 33RECh. 13 - Prob. 34RECh. 13 - Prob. 35RECh. 13 - Prob. 36RECh. 13 - Prob. 37RECh. 13 - Prob. 38RECh. 13 - In Exercises 37-40, a country is composed of four...Ch. 13 - Prob. 40RECh. 13 - Prob. 41RECh. 13 - A country has 100 seats in the congress, divided...Ch. 13 - Prob. 43RECh. 13 - Is the following statement true or false? There...
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