Pearson eText for An Introduction to Mathematical Statistics and Its Applications -- Instant Access (Pearson+)
6th Edition
ISBN: 9780137549375
Author: Richard Larsen, Morris Marx
Publisher: PEARSON+
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Chapter 2.2, Problem 27Q
(a)
To determine
The condition that must true of
(b)
To determine
The condition that must true of events A and B if
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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.
Chapter 2 Solutions
Pearson eText for An Introduction to Mathematical Statistics and Its Applications -- Instant Access (Pearson+)
Ch. 2.2 - A graduating engineer has signed up for three job...Ch. 2.2 - Three dice are tossed, one red, one blue, and one...Ch. 2.2 - An urn contains six chips numbered 1 through 6....Ch. 2.2 - Suppose that two cards are dealt from a standard...Ch. 2.2 - In the lingo of craps-shooters (where two dice are...Ch. 2.2 - A poker deck consists of fifty-two cards,...Ch. 2.2 - Let P be the set of right triangles with a 5...Ch. 2.2 - Suppose a baseball player steps to the plate with...Ch. 2.2 - A telemarketer is planning to set up a phone bank...Ch. 2.2 - Two darts are thrown at the following target: (a)...
Ch. 2.2 - A woman has her purse snatched by two teenagers....Ch. 2.2 - Consider the experiment of choosing coefficients...Ch. 2.2 - In the game of craps, the person rolling the dice...Ch. 2.2 - A probability-minded despot offers a convicted...Ch. 2.2 - Suppose that ten chips, numbered 1 through 10, are...Ch. 2.2 - Sketch the regions in the xy-plane corresponding...Ch. 2.2 - Referring to Example 2.2.7, find (AB) and (AB) if...Ch. 2.2 - Find (ABC) if A={x:0x4}, B={x:2x6} and...Ch. 2.2 - Prob. 19QCh. 2.2 - Prob. 20QCh. 2.2 - Let A be the set of five-card hands dealt from a...Ch. 2.2 - Suppose that each of the twelve letters in the...Ch. 2.2 - Let A, B, and C be any three events defined on a...Ch. 2.2 - Let A1,A2,........,Ak be any set of events defined...Ch. 2.2 - Let A, B, and C be any three events defined on a...Ch. 2.2 - Suppose that three eventsA, B, and Care de-fined...Ch. 2.2 - Prob. 27QCh. 2.2 - Let events A and B and sample space S be defined...Ch. 2.2 - A coin is tossed four times and the resulting...Ch. 2.2 - Pictured below are two organizational charts...Ch. 2.2 - During orientation week, the latest Spiderman...Ch. 2.2 - Let A and B be any two events. Use Venn diagrams...Ch. 2.2 - Let A, B, and C be any three events. Use Venn...Ch. 2.2 - Let A, B, and C be any three events. Use Venn...Ch. 2.2 - Let A and B be any two events defined on a sample...Ch. 2.2 - Use Venn diagrams to suggest an equivalent way of...Ch. 2.2 - A total of twelve hundred graduates of State Tech...Ch. 2.2 - Let A, B, and C be any three events defined on a...Ch. 2.2 - A poll conducted by a potential presidential...Ch. 2.2 - For two events A and B defined on a sample space...Ch. 2.3 - According to a family-oriented lobbying group,...Ch. 2.3 - Let A and B be any two events defined on S....Ch. 2.3 - Express the following probabilities in terms of...Ch. 2.3 - LetAandBbe two events defined on S. If the...Ch. 2.3 - Suppose that three fair dice are tossed. Let Ai be...Ch. 2.3 - Events A and B are defined on a sample space S...Ch. 2.3 - Let A1,A2....,An be a series of events for which...Ch. 2.3 - Draw the Venn diagrams that would correspond to...Ch. 2.3 - In the game of odd man out each player tosses a...Ch. 2.3 - An urn contains twenty-four chips, numbered 1...Ch. 2.3 - If States football team has a 10% chance of...Ch. 2.3 - Let events A1 and A2 are such that A1A2=S and...Ch. 2.3 - Prob. 13QCh. 2.3 - Prob. 14QCh. 2.3 - A coin is to be tossed four times. Define events X...Ch. 2.3 - Two dice are tossed. Assume that each possible...Ch. 2.3 - Let A, B, and C be three events defined on a...Ch. 2.3 - Lucy is currently running two dot-com scams out of...Ch. 2.4 - Suppose that two fair dice are tossed. What is the...Ch. 2.4 - Find P(AB) if P(A)=0.2,P(B)=0.4, and...Ch. 2.4 - If P(AB)P(A), show that P(BA)P(B).Ch. 2.4 - Let A and B be two events such that...Ch. 2.4 - Suppose that in Example 2.4.2 we ignored the ages...Ch. 2.4 - Two events, A and B, are defined on a sample space...Ch. 2.4 - An urn contains one red chip and one white chip....Ch. 2.4 - Given that P(A)=a and P(B)=b, show that P(AB)a+b1bCh. 2.4 - An urn contains one white chip and a second chip...Ch. 2.4 - Suppose events A and B are such that P(AB)=0.1 and...Ch. 2.4 - One hundred voters were asked their opinions of...Ch. 2.4 - A fair coin is tossed three times. What is the...Ch. 2.4 - Two fair dice are rolled. What is the probability...Ch. 2.4 - Four cards are dealt from a standard 52-card poker...Ch. 2.4 - Prob. 15QCh. 2.4 - Given that P(A)+P(B)=0.9,P(AB)=0.5, and...Ch. 2.4 - Let A and B be two events defined on a sample...Ch. 2.4 - Suppose two dice are rolled. Assume that each...Ch. 2.4 - According to your neighborhood bookie, five horses...Ch. 2.4 - Andy, Bob, and Charley have all been serving time...Ch. 2.4 - An urn contains six white chips, four black chips,...Ch. 2.4 - A man has n keys on a key ring, one of which opens...Ch. 2.4 - Your favorite college football team has had a good...Ch. 2.4 - One chip is drawn at random from an urn that...Ch. 2.4 - A toy manufacturer buys ball bearings from three...Ch. 2.4 - A fair coin is tossed. If a head turns up, a fair...Ch. 2.4 - Foreign policy experts estimate that the...Ch. 2.4 - A telephone solicitor is responsible for...Ch. 2.4 - If men constitute 47% of the population and tell...Ch. 2.4 - Urn I contains three red chips and one white chip....Ch. 2.4 - Medical records show that 0.01% of the general...Ch. 2.4 - Prob. 32QCh. 2.4 - In an upstate congressional race, the incumbent...Ch. 2.4 - An urn contains forty red chips and sixty white...Ch. 2.4 - A study has shown that seven out of ten people...Ch. 2.4 - Based on pretrial speculation, the probability...Ch. 2.4 - Prob. 37QCh. 2.4 - The governor of a certain state has decided to...Ch. 2.4 - Following are the percentages of students of State...Ch. 2.4 - Urn I contains two white chips and one red chip;...Ch. 2.4 - Urn I contains three red chips and five white...Ch. 2.4 - A dashboard warning light is supposed to flash red...Ch. 2.4 - Building permits were issued last year to three...Ch. 2.4 - Two sections of a senior probability course are...Ch. 2.4 - A liquor store owner is willing to cash personal...Ch. 2.4 - Brett and Margo have each thought about murdering...Ch. 2.4 - Josh takes a twenty-question multiple-choice exam...Ch. 2.4 - Prob. 48QCh. 2.4 - At State University, 30% of the students are...Ch. 2.4 - Prob. 50QCh. 2.4 - When Zach wants to contact his girlfriend and he...Ch. 2.4 - A dot-com company ships products from three...Ch. 2.4 - A desk has three drawers. The first contains two...Ch. 2.4 - An automobile insurance company has compiled the...Ch. 2.5 - Suppose that P(AB)=0.2, P(A)=0.6, and P(B)=0.5....Ch. 2.5 - Spike is not a terribly bright student. His...Ch. 2.5 - Two fair dice are rolled. What is the probability...Ch. 2.5 - Emma and Josh have just gotten engaged. What is...Ch. 2.5 - Dana and Cathy are playing tennis. The probability...Ch. 2.5 - Three points, X1,X2andX3, are chosen at random in...Ch. 2.5 - Suppose that P(A)=14andP(B)=18 (a) What does P(AB)...Ch. 2.5 - Suppose that events A, B, and C are independent....Ch. 2.5 - A fair coin is tossed four times. What is the...Ch. 2.5 - Suppose that two cards are drawn simultaneously...Ch. 2.5 - Suppose that two fair dice (one red and one green)...Ch. 2.5 - A roulette wheel has thirty-six numbers colored...Ch. 2.5 - How many probability equations need to be...Ch. 2.5 - Prob. 14QCh. 2.5 - In a roll of a pair of fair dice (one red and one...Ch. 2.5 - On her way to work, a commuter encounters four...Ch. 2.5 - School board officials are debating whether to...Ch. 2.5 - Consider the following four-switch circuit: If all...Ch. 2.5 - A fast-food chain is running a new promotion. For...Ch. 2.5 - Players A, B, and C toss a fair coin in order. The...Ch. 2.5 - Prob. 21QCh. 2.5 - According to an advertising study, 15% of...Ch. 2.5 - A fair die is rolled and then n fair coins are...Ch. 2.5 - Prob. 24QCh. 2.5 - If two fair dice are tossed, what is the smallest...Ch. 2.5 - Prob. 26QCh. 2.5 - An urn contains w white chips, b black chips, and...Ch. 2.5 - Prob. 28QCh. 2.5 - A computer is instructed to generate a random...Ch. 2.5 - Prob. 30QCh. 2.5 - Stanleys statistics seminar is graded on a...Ch. 2.5 - What is the smallest number of switches wired in...Ch. 2.6 - Achemical engineer wishes to observe the effects...Ch. 2.6 - A coded message from a CIA operative to his...Ch. 2.6 - How many terms will be included in the expansion...Ch. 2.6 - Suppose that the format for license plates in a...Ch. 2.6 - How many integers between 100 and 999 have...Ch. 2.6 - A fast-food restaurant offers customers a choice...Ch. 2.6 - In baseball there are twenty-four different...Ch. 2.6 - Recall the postal zip codes described in Example...Ch. 2.6 - Arestaurant offers a choice of four appetizers,...Ch. 2.6 - An octave contains twelve distinct notes (on a...Ch. 2.6 - Residents of a condominium have an automatic...Ch. 2.6 - In international Morse code, each letter in the...Ch. 2.6 - The decimal number corresponding to a sequence of...Ch. 2.6 - Given the letters in the word ZOMBIESin how many...Ch. 2.6 - Suppose that two cards are drawnin orderfrom a...Ch. 2.6 - Monicas vacation plans require that she fly from...Ch. 2.6 - The board of a large corporation has six members...Ch. 2.6 - How many ways can a set of four tires be put on a...Ch. 2.6 - Use Stirlings formula to approximate 30!.(Note:...Ch. 2.6 - The nine members of the music faculty baseball...Ch. 2.6 - A three-digit number is to be formed from the...Ch. 2.6 - Four men and four women are to be seated in a row...Ch. 2.6 - An engineer needs to take three technical...Ch. 2.6 - How many ways can a twelve-member cheerleading...Ch. 2.6 - Suppose that a seemingly interminable German opera...Ch. 2.6 - A new horror movie, Friday the 13th, Part X, will...Ch. 2.6 - Suppose that ten people, including you and a...Ch. 2.6 - Use an induction argument to prove Theo-rem 2.6.1....Ch. 2.6 - In how many ways can a pack of fifty-two cards be...Ch. 2.6 - If the definition of n! is to hold for all...Ch. 2.6 - The crew of Apollo 17 consisted of a pilot, a...Ch. 2.6 - Uncle Harry and Aunt Minnie will both be attending...Ch. 2.6 - In how many ways can the digits 1 through 9 be...Ch. 2.6 - Which state name can generate more permutations,...Ch. 2.6 - How many numbers greater than four million can...Ch. 2.6 - An interior decorator is trying to arrange a shelf...Ch. 2.6 - Four Nigerians (A, B, C, D), three Chinese (#, ,...Ch. 2.6 - How many ways can the letters in the word...Ch. 2.6 - A tennis tournament has a field of 2n entrants,...Ch. 2.6 - Prob. 40QCh. 2.6 - In how many ways can the letters of the word...Ch. 2.6 - In how many ways can the word ABRACADABRA be...Ch. 2.6 - Prob. 43QCh. 2.6 - Prob. 44QCh. 2.6 - Prob. 45QCh. 2.6 - Prob. 46QCh. 2.6 - In how many ways can the letters of the word...Ch. 2.6 - Prob. 48QCh. 2.6 - Prob. 49QCh. 2.6 - How many straight lines can be drawn between five...Ch. 2.6 - The Alpha Beta Zeta sorority is trying to fill a...Ch. 2.6 - A boat has a crew of eight: Two of those eight can...Ch. 2.6 - Nine students, five men and four women, interview...Ch. 2.6 - The final exam in History 101 consists of five...Ch. 2.6 - Ten basketball players meet in the school gym for...Ch. 2.6 - Your statistics teacher announces a twenty-page...Ch. 2.6 - In how many ways can the letters in MI S S I S S I...Ch. 2.6 - Prove that (kn+1)=(kn)+(k1n) directly without...Ch. 2.6 - Find a recursion formula for (k+1n) in terms of...Ch. 2.6 - Show that n(n1)2n2=k=2nk(k1)Cnk.Ch. 2.6 - Prob. 61QCh. 2.6 - Prob. 62QCh. 2.6 - Compare the coefficients of tk in...Ch. 2.7 - Ten equally qualified marketing assistants are...Ch. 2.7 - An urn contains six chips, numbered 1 through 6....Ch. 2.7 - Anurn contains twenty chips, numbered1 through 20....Ch. 2.7 - A bridge hand (thirteen cards) is dealt from a...Ch. 2.7 - Consider a set of ten urns, nine of which contain...Ch. 2.7 - A committee of fifty politicians is to be chosen...Ch. 2.7 - Suppose that n fair dice are rolled. What are the...Ch. 2.7 - Five fair dice are rolled. What is the probability...Ch. 2.7 - Imagine that the test tube pictured contains 2n...Ch. 2.7 - Does a monkey have a better chance of rearranging...Ch. 2.7 - An apartment building has eight floors. If seven...Ch. 2.7 - If the letters in the phrase A ROLLING STONE...Ch. 2.7 - Suppose each of ten sticks is broken into a long...Ch. 2.7 - Six dice are rolled one time. What is the...Ch. 2.7 - Suppose that a randomly selected group of k people...Ch. 2.7 - Prob. 16QCh. 2.7 - Dana is not the worlds best poker player. Dealt a...Ch. 2.7 - A poker player is dealt a 7 of diamonds, a queen...Ch. 2.7 - Tim is dealt a 4 of clubs, a 6 of hearts, an 8 of...Ch. 2.7 - Five cards are dealt from a standard 52-card deck....Ch. 2.7 - Nine cards are dealt from a 52-card deck. Write a...Ch. 2.7 - A coke hand in bridge is one where none of the...Ch. 2.7 - A pinochle deck has forty-eight cards, two of each...
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