Mathematical Statistics with Applications
7th Edition
ISBN: 9780495110811
Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer
Publisher: Cengage Learning
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Textbook Question
Chapter 5.2, Problem 1E
Contracts for two construction jobs are randomly assigned to one or more of three firms, A, B, and C. Let Y1 denote the number of contracts assigned to firm A and Y2 the number of contracts assigned to firm B. Recall that each firm can receive 0, 1, or 2 contracts.
- a Find the joint
probability function for Y1 and Y2. - b Find F(1, 0).
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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 5 Solutions
Mathematical Statistics with Applications
Ch. 5.2 - Contracts for two construction jobs are randomly...Ch. 5.2 - Three balanced coins are tossed independently. One...Ch. 5.2 - Of nine executives in a business firm, four are...Ch. 5.2 - Given here is the joint probability function...Ch. 5.2 - Refer to Example 5.4. The joint density of Y1, the...Ch. 5.2 - Prob. 6ECh. 5.2 - Let Y1 and Y2 have joint density function...Ch. 5.2 - Prob. 8ECh. 5.2 - Prob. 9ECh. 5.2 - An environmental engineer measures the amount (by...
Ch. 5.2 - Suppose that Y1 and Y2 are uniformly distributed...Ch. 5.2 - Prob. 12ECh. 5.2 - Prob. 13ECh. 5.2 - Prob. 14ECh. 5.2 - The management at a fast-food outlet is interested...Ch. 5.2 - Let Y1 and Y2 denote the proportions of time (out...Ch. 5.2 - Let (Y1, Y2) denote the coordinates of a point...Ch. 5.2 - Prob. 18ECh. 5.3 - In Exercise 5.1, we determined that the joint...Ch. 5.3 - Refer to Exercise 5.2. a Derive the marginal...Ch. 5.3 - In Exercise 5.3, we determined that the joint...Ch. 5.3 - In Exercise 5.4, you were given the following...Ch. 5.3 - In Example 5.4 and Exercise 5.5, we considered the...Ch. 5.3 - Prob. 24ECh. 5.3 - Prob. 25ECh. 5.3 - Prob. 26ECh. 5.3 - Prob. 27ECh. 5.3 - In Exercise 5.10, we proved that...Ch. 5.3 - Prob. 29ECh. 5.3 - In Exercise 5.12, we were given the following...Ch. 5.3 - In Exercise 5.13, the joint density function of Y1...Ch. 5.3 - Prob. 32ECh. 5.3 - Suppose that Y1 is the total time between a...Ch. 5.3 - Prob. 34ECh. 5.3 - Prob. 35ECh. 5.3 - Prob. 36ECh. 5.3 - Prob. 37ECh. 5.3 - Let Y1 denote the weight (in tons) of a bulk item...Ch. 5.3 - Prob. 39ECh. 5.3 - Prob. 40ECh. 5.3 - Prob. 41ECh. 5.3 - Prob. 42ECh. 5.4 - Let Y1 and Y2 have joint density function f(y1,...Ch. 5.4 - Prob. 44ECh. 5.4 - Prob. 45ECh. 5.4 - Prob. 46ECh. 5.4 - In Exercise 5.3, we determined that the joint...Ch. 5.4 - In Exercise 5.4, you were given the following...Ch. 5.4 - In Example 5.4 and Exercise 5.5, we considered the...Ch. 5.4 - Prob. 50ECh. 5.4 - Prob. 51ECh. 5.4 - Prob. 52ECh. 5.4 - Prob. 53ECh. 5.4 - Prob. 54ECh. 5.4 - Prob. 55ECh. 5.4 - In Exercise 5.12, we were given the following...Ch. 5.4 - Prob. 57ECh. 5.4 - Suppose that the random variables Y1 and Y2 have...Ch. 5.4 - If Y1 is the total time between a customers...Ch. 5.4 - Prob. 60ECh. 5.4 - Prob. 61ECh. 5.4 - Prob. 62ECh. 5.4 - Let Y1 and Y2 be independent exponentially...Ch. 5.4 - Prob. 64ECh. 5.4 - Prob. 65ECh. 5.4 - Let F1(y1) and F2(y2) be two distribution...Ch. 5.4 - Prob. 67ECh. 5.4 - Prob. 68ECh. 5.4 - The length of life Y for fuses of a certain type...Ch. 5.4 - A bus arrives at a bus stop at a uniformly...Ch. 5.4 - Prob. 71ECh. 5.6 - In Exercise 5.1, we determined that the joint...Ch. 5.6 - Prob. 73ECh. 5.6 - Refer to Exercises 5.6, 5.24, and 5.50. Suppose...Ch. 5.6 - Prob. 75ECh. 5.6 - Prob. 76ECh. 5.6 - Prob. 77ECh. 5.6 - Prob. 78ECh. 5.6 - Suppose that, as in Exercise 5.11, Y1 and Y2 are...Ch. 5.6 - In Exercise 5.16, Y1 and Y2 denoted the...Ch. 5.6 - In Exercise 5.18, Y1 and Y2 denoted the lengths of...Ch. 5.6 - In Exercise 5.38, we determined that the joint...Ch. 5.6 - Prob. 83ECh. 5.6 - In Exercise 5.62, we considered two individuals...Ch. 5.6 - Prob. 85ECh. 5.6 - Prob. 86ECh. 5.6 - Prob. 87ECh. 5.6 - Prob. 88ECh. 5.7 - In Exercise 5.1, we determined that the joint...Ch. 5.7 - Prob. 90ECh. 5.7 - In Exercise 5.8, we derived the fact that...Ch. 5.7 - Prob. 92ECh. 5.7 - Suppose that, as in Exercises 5.11 and 5.79, Y1...Ch. 5.7 - Prob. 94ECh. 5.7 - Prob. 95ECh. 5.7 - Prob. 96ECh. 5.7 - The random variables Y1 and Y2 are such that E(Y1)...Ch. 5.7 - Prob. 98ECh. 5.7 - Prob. 99ECh. 5.7 - Let Z be a standard normal random variable and let...Ch. 5.7 - Prob. 101ECh. 5.8 - A firm purchases two types of industrial...Ch. 5.8 - Prob. 103ECh. 5.8 - Prob. 104ECh. 5.8 - Prob. 105ECh. 5.8 - In Exercise 5.9, we determined that...Ch. 5.8 - In Exercise 5.12, we were given the following...Ch. 5.8 - If Y1 is the total time between a customers...Ch. 5.8 - In Exercise 5.16, Y1 and Y2 denoted the...Ch. 5.8 - Suppose that Y1 and Y2 have correlation...Ch. 5.8 - Prob. 111ECh. 5.8 - In Exercise 5.18, Y1 and Y2 denoted the lengths of...Ch. 5.8 - A retail grocery merchant figures that her daily...Ch. 5.8 - For the daily output of an industrial operation,...Ch. 5.8 - Prob. 115ECh. 5.8 - Prob. 116ECh. 5.8 - A population of N alligators is to be sampled in...Ch. 5.8 - Prob. 118ECh. 5.9 - A learning experiment requires a rat to run a maze...Ch. 5.9 - Prob. 120ECh. 5.9 - Refer to Exercise 5.117. Suppose that the number N...Ch. 5.9 - The weights of a population of mice fed on a...Ch. 5.9 - Prob. 123ECh. 5.9 - The typical cost of damages caused by a fire in a...Ch. 5.9 - When commercial aircraft are inspected, wing...Ch. 5.9 - Prob. 126ECh. 5.9 - Prob. 127ECh. 5.10 - Let Y1 and Y2 have a bivariate normal...Ch. 5.10 - Prob. 129ECh. 5.10 - Prob. 130ECh. 5.10 - Prob. 131ECh. 5.10 - Prob. 132ECh. 5.11 - Prob. 133ECh. 5.11 - Prob. 134ECh. 5.11 - In Exercise 5.41, we considered a quality control...Ch. 5.11 - In Exercise 5.42, the number of defects per yard...Ch. 5.11 - In Exercise 5.38, we assumed that Y1, the weight...Ch. 5.11 - Assume that Y denotes the number of bacteria per...Ch. 5.11 - Prob. 139ECh. 5.11 - Prob. 140ECh. 5.11 - Let Y1 have an exponential distribution with mean ...Ch. 5.11 - Prob. 142ECh. 5.11 - Prob. 143ECh. 5 - Prove Theorem 5.9 when Y1 and Y2 are independent...Ch. 5 - Prob. 145SECh. 5 - Prob. 146SECh. 5 - Two friends are to meet at the library. Each...Ch. 5 - Prob. 148SECh. 5 - Prob. 149SECh. 5 - Prob. 150SECh. 5 - The lengths of life Y for a type of fuse has an...Ch. 5 - In the production of a certain type of copper, two...Ch. 5 - Suppose that the number of eggs laid by a certain...Ch. 5 - In a clinical study of a new drug formulated to...Ch. 5 - Prob. 155SECh. 5 - Refer to Exercise 5.86. Suppose that Z is a...Ch. 5 - Prob. 157SECh. 5 - Prob. 158SECh. 5 - Prob. 159SECh. 5 - Prob. 160SECh. 5 - Suppose that we are to observe two independent...Ch. 5 - Prob. 162SECh. 5 - Prob. 163SECh. 5 - Prob. 164SECh. 5 - Prob. 165SECh. 5 - Prob. 166SECh. 5 - Prob. 167SE
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