Mathematics: A Practical Odyssey
8th Edition
ISBN: 9781305104174
Author: David B. Johnson, Thomas A. Mowry
Publisher: Cengage Learning
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Chapter 2.3, Problem 45E
Find the value of
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PEER REPLY 1:
Choose a classmate's Main Post and review their decision making process.
1. Choose a risk level for each of the states of nature (assign a probability
value to each).
2. Explain why each risk level is chosen.
3. Which alternative do you believe would be the best based on the maximum
EMV?
4. Do you feel determining the expected value with perfect information
(EVWPI) is worthwhile in this situation? Why or why not?
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.
Chapter 2 Solutions
Mathematics: A Practical Odyssey
Ch. 2.1 - Prob. 1ECh. 2.1 - Suppose A={2,5,7,9,13,25,26}. a. Find n(A) b. True...Ch. 2.1 - Prob. 3ECh. 2.1 - Prob. 4ECh. 2.1 - Prob. 5ECh. 2.1 - Prob. 6ECh. 2.1 - Prob. 7ECh. 2.1 - Prob. 8ECh. 2.1 - Prob. 9ECh. 2.1 - Prob. 10E
Ch. 2.1 - Prob. 11ECh. 2.1 - Prob. 12ECh. 2.1 - Prob. 13ECh. 2.1 - Prob. 14ECh. 2.1 - Prob. 15ECh. 2.1 - Prob. 16ECh. 2.1 - Prob. 17ECh. 2.1 - Prob. 18ECh. 2.1 - Prob. 19ECh. 2.1 - Prob. 20ECh. 2.1 - Prob. 21ECh. 2.1 - Prob. 22ECh. 2.1 - Prob. 23ECh. 2.1 - Prob. 24ECh. 2.1 - Prob. 25ECh. 2.1 - Prob. 26ECh. 2.1 - Suppose n(U)=150, n(A)=37, and n(B)=84. a. If...Ch. 2.1 - Prob. 28ECh. 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 - Prob. 38ECh. 2.1 - Prob. 39ECh. 2.1 - Prob. 40ECh. 2.1 - Prob. 41ECh. 2.1 - Prob. 42ECh. 2.1 - Prob. 43ECh. 2.1 - Prob. 44ECh. 2.1 - Prob. 45ECh. 2.1 - Prob. 46ECh. 2.1 - Prob. 47ECh. 2.1 - Prob. 48ECh. 2.1 - Prob. 49ECh. 2.1 - Prob. 50ECh. 2.1 - Prob. 51ECh. 2.1 - Prob. 52ECh. 2.1 - Prob. 53ECh. 2.1 - Prove the Cardinal Number Rule for the Complement...Ch. 2.1 - Prob. 55ECh. 2.1 - Prob. 56ECh. 2.1 - Answer the following questions using complete...Ch. 2.1 - Prob. 58ECh. 2.1 - Prob. 59ECh. 2.1 - Prob. 60ECh. 2.1 - Prob. 61ECh. 2.1 - Prob. 62ECh. 2.1 - Prob. 63ECh. 2.1 - Prob. 64ECh. 2.1 - Prob. 65ECh. 2.1 - Prob. 66ECh. 2.1 - Prob. 67ECh. 2.1 - Prob. 68ECh. 2.1 - The following questions are modeled after those...Ch. 2.2 - A survey of 200 people yielded the following...Ch. 2.2 - A survey of 300 workers yielded the following...Ch. 2.2 - The records of 1,492 high school graduates were...Ch. 2.2 - A department store surveyed 428 shoppers, and the...Ch. 2.2 - In a survey, 674 adults were asked what television...Ch. 2.2 - A survey asked 816 college freshmen whether they...Ch. 2.2 - A local 4-H club surveyed its members, and the...Ch. 2.2 - A local anime fan club surveyed its members...Ch. 2.2 - A recent survey of w shoppers that is, n(U)=w...Ch. 2.2 - A recent transportation survey of w urban...Ch. 2.2 - A consumer survey was conducted to examine...Ch. 2.2 - In a recent survey of monetary donations made by...Ch. 2.2 - Recently, Lady Gaga, Arcade Fire, and Skrillex had...Ch. 2.2 - Dr. Hawk works in an allergy clinic, and his...Ch. 2.2 - When the member of the Eye and I photo club...Ch. 2.2 - After leaving the polls, many people are asked how...Ch. 2.2 - In a recent survey consumer were asked where they...Ch. 2.2 - A company that specializes in language tutorial...Ch. 2.2 - In a recent survey, people were asked which radio...Ch. 2.2 - In a recent health insurance survey, employee at...Ch. 2.2 - A survey of 136 pet owners yielded the following...Ch. 2.2 - An exit poll of 300 votes yielded the following...Ch. 2.2 - Prob. 23ECh. 2.2 - Prob. 24ECh. 2.2 - Prob. 25ECh. 2.2 - Prob. 26ECh. 2.2 - Prob. 27ECh. 2.2 - Prob. 28ECh. 2.2 - Prob. 29ECh. 2.2 - Prob. 30ECh. 2.2 - Prob. 31ECh. 2.2 - Prob. 32ECh. 2.2 - Using Venn diagrams, prove De Morgans law (AB)=AB.Ch. 2.2 - Prob. 34ECh. 2.2 - Use the data in Figure 2.34 to complete Exercise...Ch. 2.2 - Use the data in Figure 2.34 to complete Exercise...Ch. 2.2 - Prob. 37ECh. 2.2 - Prob. 38ECh. 2.2 - Use the data in Figure 2.34 to complete Exercise...Ch. 2.2 - Prob. 40ECh. 2.2 - If a person has type B blood, what blood types may...Ch. 2.2 - Prob. 42ECh. 2.2 - If a person has type O blood, what blood types may...Ch. 2.2 - Answer the following questions using complete...Ch. 2.2 - Prob. 45ECh. 2.2 - Prob. 46ECh. 2.2 - Prob. 47ECh. 2.2 - Prob. 48ECh. 2.2 - Exercises 4652 refer to the following: A nonprofit...Ch. 2.2 - Prob. 50ECh. 2.2 - Prob. 51ECh. 2.2 - Prob. 52ECh. 2.2 - Prob. 53ECh. 2.3 - Prob. 1ECh. 2.3 - Prob. 2ECh. 2.3 - Jamie has decided to buy either a Mega or a Better...Ch. 2.3 - Prob. 4ECh. 2.3 - If you buy three pairs of jeans, four sweaters,...Ch. 2.3 - A certain model of automobiles is available in six...Ch. 2.3 - To fulfill certain requirements for a degree, a...Ch. 2.3 - To fulfill a requirement for a literature class, a...Ch. 2.3 - A sporting goods store has fourteen lines of snow...Ch. 2.3 - An audio equipment store has ten different...Ch. 2.3 - A cafeteria offers a complete dinner that includes...Ch. 2.3 - A sandwich shop offers a U-Chooz special...Ch. 2.3 - How many different Social Security numbers are...Ch. 2.3 - To use an automated teller machine ATM, a customer...Ch. 2.3 - Every book published has an International Standard...Ch. 2.3 - How many different Zip Codes are possible using a...Ch. 2.3 - Telephone area codes are three-digit numbers of...Ch. 2.3 - Major credit cards such as VISA and MasterCard...Ch. 2.3 - The serial number on a dollar bill consists of a...Ch. 2.3 - The serial number on a new twenty-dollar bill...Ch. 2.3 - Each student at State University has a student ID...Ch. 2.3 - Each student at State College has a student ID...Ch. 2.3 - In Exercises 2338, find the indicated value. 4!Ch. 2.3 - In Exercises 2338, find the indicated value. 5!Ch. 2.3 - In Exercises 2338, find the indicated value. 10!Ch. 2.3 - In Exercises 2338, find the indicated value. 8!Ch. 2.3 - In Exercises 2338, find the indicated value. 20!Ch. 2.3 - In Exercises 2338, find the indicated value. 25!Ch. 2.3 - In Exercises 2338, find the indicated value. 6!4!Ch. 2.3 - In Exercises 2338, find the indicated value. 8!6!Ch. 2.3 - In Exercises 2338, find the indicated value. a....Ch. 2.3 - In Exercises 2338, find the indicated value. a....Ch. 2.3 - In Exercises 2338, find the indicated value....Ch. 2.3 - In Exercises 2338, find the indicated value....Ch. 2.3 - In Exercises 2338, find the indicated value....Ch. 2.3 - In Exercises 2338, find the indicated value....Ch. 2.3 - In Exercises 2338, find the indicated value....Ch. 2.3 - In Exercises 2338, find the indicated value....Ch. 2.3 - Find the value of n!(nr)!, when n=16 and r=14.Ch. 2.3 - Find the value of n!(nr)!, when n=19 and r=16.Ch. 2.3 - Find the value of n!(nr)!, when n=5 and r=5.Ch. 2.3 - Find the value of n!(nr)!, when n=r.Ch. 2.3 - Find the value of n!(nr)!r!, when n=7 and r=3.Ch. 2.3 - Find the value of n!(nr)!r!, when n=7 and r=4.Ch. 2.3 - Find the value of n!(nr)!r!, when n=5 and r=5.Ch. 2.3 - Find the value of n!(nr)!r!, when n=r.Ch. 2.3 - Answer the following questions using complete...Ch. 2.3 - Answer the following questions using complete...Ch. 2.3 - Answer the following questions using complete...Ch. 2.3 - The following questions are modeled after those...Ch. 2.3 - Prob. 51ECh. 2.3 - The following questions are modeled after those...Ch. 2.3 - Prob. 53ECh. 2.3 - Prob. 54ECh. 2.4 - In Exercises 112, find the indicated value: a. 7P3...Ch. 2.4 - In Exercises 112, find the indicated value: a. 8P4...Ch. 2.4 - In Exercises 112, find the indicated value: a. 5P5...Ch. 2.4 - In Exercises 112, find the indicated value: a. 9P0...Ch. 2.4 - In Exercises 112, find the indicated value: a....Ch. 2.4 - In Exercises 112, find the indicated value: a....Ch. 2.4 - In Exercises 112, find the indicated value: a....Ch. 2.4 - In Exercises 112, find the indicated value: a....Ch. 2.4 - In Exercises 112, find the indicated value: a....Ch. 2.4 - In Exercises 112, find the indicated value: a. xP1...Ch. 2.4 - In Exercises 112, find the indicated value: a. xP2...Ch. 2.4 - In Exercises 112, find the indicated value: a....Ch. 2.4 - a. Find 3P2. b. List all of the permutations of...Ch. 2.4 - a. Find 3C2. b. List all of the combinations of...Ch. 2.4 - Prob. 15ECh. 2.4 - a. Find 4P2. b. List all of the permutations of...Ch. 2.4 - Prob. 17ECh. 2.4 - An English class consists of twenty-three students...Ch. 2.4 - In how many ways can the letters in the word...Ch. 2.4 - A committee of four is to be selected from a group...Ch. 2.4 - A softball league has thirteen teams. If every...Ch. 2.4 - In a group of eighteen people, each person shakes...Ch. 2.4 - A softball league has thirteen teams. How many...Ch. 2.4 - Three hundred people buy raffle tickets. Three...Ch. 2.4 - A group of nine women and six men must select a...Ch. 2.4 - A group of ten seniors, eight juniors, six...Ch. 2.4 - Exercise2732, refer to a deck of fifty-two playing...Ch. 2.4 - Exercise2732, refer to a deck of fifty-two playing...Ch. 2.4 - Exercise2732, refer to a deck of fifty-two playing...Ch. 2.4 - Exercise2732, refer to a deck of fifty-two playing...Ch. 2.4 - How many five-card poker hands containing two pair...Ch. 2.4 - Exercise2732, refer to a deck of fifty-two playing...Ch. 2.4 - Exercises 3344 refer to lotteries; the order in...Ch. 2.4 - Exercises 3344 refer to lotteries; the order in...Ch. 2.4 - A 5/36 lottery requires choosing five of the...Ch. 2.4 - Exercises 3344 refer to lotteries; the order in...Ch. 2.4 - Exercises 3344 refer to lotteries; the order in...Ch. 2.4 - Exercises 3344 refer to lotteries; the order in...Ch. 2.4 - Over forty states participate in Powerball, a...Ch. 2.4 - Over forty states participate in Mega Millions, a...Ch. 2.4 - Exercises 33-44 refer to lotteries; the order in...Ch. 2.4 - Exercises 33-44 refer to lotteries; the order in...Ch. 2.4 - Exercises 33-44 refer to lotteries; the order in...Ch. 2.4 - Exercises 33-44 refer to lotteries; the order in...Ch. 2.4 - a. Find the sum of the entries in the first row of...Ch. 2.4 - a. Add adjacent entries of the sixth row of...Ch. 2.4 - Use Pascals Triangle to answer the following. a....Ch. 2.4 - Given the set S={a, b, c, d}, answer the...Ch. 2.4 - In Exercise 49-56, find the number of permutation...Ch. 2.4 - In Exercise 49-56, find the number of permutation...Ch. 2.4 - In Exercise 49-56, find the number of permutation...Ch. 2.4 - In Exercise 49-56, find the number of permutation...Ch. 2.4 - In Exercise 49-56, find the number of permutation...Ch. 2.4 - In Exercises 49-56, find the number of permutation...Ch. 2.4 - In Exercises 49-56, find the number of permutation...Ch. 2.4 - In Exercise 49-56, find the number of permutations...Ch. 2.4 - The words in each of Exercises 57-60 are homonyms...Ch. 2.4 - The words in each of Exercises 57-60 are homonyms...Ch. 2.4 - The words in each of Exercises 57-60 are homonyms...Ch. 2.4 - The words in each of Exercises 57-60 are homonyms...Ch. 2.4 - Prob. 61ECh. 2.4 - Prob. 62ECh. 2.4 - Exercise 6367 refer to the following: A baseball...Ch. 2.4 - Prob. 64ECh. 2.4 - Prob. 65ECh. 2.4 - Prob. 66ECh. 2.4 - Prob. 67ECh. 2.4 - Prob. 68ECh. 2.5 - Prob. 1ECh. 2.5 - In Exercises 1-10, find the cardinal numbers of...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 - Prob. 10ECh. 2.5 - Prob. 11ECh. 2.5 - Prob. 12ECh. 2.5 - Prob. 13ECh. 2.5 - Prob. 14ECh. 2.5 - Prob. 15ECh. 2.5 - Consider the following one-to-one correspondence...Ch. 2.5 - Prob. 17ECh. 2.5 - Prob. 18ECh. 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 - Prob. 27ECh. 2.5 - Prob. 28ECh. 2.CR - Prob. 1CRCh. 2.CR - Prob. 2CRCh. 2.CR - Prob. 3CRCh. 2.CR - Prob. 4CRCh. 2.CR - Prob. 5CRCh. 2.CR - Prob. 6CRCh. 2.CR - Prob. 7CRCh. 2.CR - Prob. 8CRCh. 2.CR - Prob. 9CRCh. 2.CR - A survey of 1,000 college seniors yielded the...Ch. 2.CR - A survey of recent college graduates yielded the...Ch. 2.CR - A local anime fan club surveyed 67 of its members...Ch. 2.CR - An exit poll yielded following information...Ch. 2.CR - Prob. 14CRCh. 2.CR - Prob. 15CRCh. 2.CR - Prob. 16CRCh. 2.CR - Prob. 17CRCh. 2.CR - A certain model of pickup truck is available in...Ch. 2.CR - Each student at State University has a student ID...Ch. 2.CR - Prob. 20CRCh. 2.CR - Prob. 21CRCh. 2.CR - Prob. 22CRCh. 2.CR - A group of ten women and twelve men must select a...Ch. 2.CR - Prob. 24CRCh. 2.CR - Prob. 25CRCh. 2.CR - Using a standard deck of fifty-two cards no...Ch. 2.CR - Prob. 27CRCh. 2.CR - A 6/42 lottery requires choosing six of the...Ch. 2.CR - Prob. 29CRCh. 2.CR - Prob. 30CRCh. 2.CR - Prob. 31CRCh. 2.CR - Prob. 32CRCh. 2.CR - Prob. 33CRCh. 2.CR - Prob. 34CRCh. 2.CR - Prob. 35CRCh. 2.CR - Prob. 36CRCh. 2.CR - Prob. 37CRCh. 2.CR - Consider the following one to one correspondence...Ch. 2.CR - Prob. 39CRCh. 2.CR - Prob. 40CRCh. 2.CR - Prob. 41CRCh. 2.CR - Prob. 42CRCh. 2.CR - Prob. 43CRCh. 2.CR - Prob. 44CRCh. 2.CR - Prob. 45CRCh. 2.CR - Prob. 46CRCh. 2.CR - Prob. 47CRCh. 2.CR - Prob. 48CR
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