An Introduction to Mathematical Statistics and Its Applications (6th Edition)
6th Edition
ISBN: 9780134114217
Author: Richard J. Larsen, Morris L. Marx
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
Chapter 5.6, Problem 9Q
To determine
To prove:
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A test consists of 10 questions made of 5 answers with only one correct answer. To pass the test, a student must answer at least 8 questions correctly. (a) If a student guesses on each question, what is the probability that the student passes the test? (b) Find the mean and standard deviation of the number of correct answers. (c) Is it unusual for a student to pass the test by guessing? Explain.
In a group of 40 people, 35% have never been abroad. Two people are selected at random without replacement and are asked about their past travel experience. a. Is this a binomial experiment? Why or why not? What is the probability that in a random sample of 2, no one has been abroad? b. What is the probability that in a random sample of 2, at least one has been abroad?
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
An Introduction to Mathematical Statistics and Its Applications (6th Edition)
Ch. 5.2 - A random sample of size...Ch. 5.2 - The number of red chips and white chips in an urn...Ch. 5.2 - Use the sample y1=8.2,y2=9.1,y3=10.6, and y4=4.9...Ch. 5.2 - Suppose a random sample of size n is drawn from...Ch. 5.2 - Given that y1=2.3,y2=1.9, and y3=4.6 is a random...Ch. 5.2 - Use the method of maximum likelihood to estimate ...Ch. 5.2 - An engineer is creating a project scheduling...Ch. 5.2 - The following data show the number of occupants in...Ch. 5.2 - For the Major League Baseball seasons from 1950...Ch. 5.2 - (a) Based on the random sample...
Ch. 5.2 - Find the maximum likelihood estimate for in the...Ch. 5.2 - A random sample of size n is taken from the pdf...Ch. 5.2 - If the random variable Y denotes an individuals...Ch. 5.2 - For the negative binomial pdf...Ch. 5.2 - The exponential pdf is a measure of lifetimes of...Ch. 5.2 - Suppose a random sample of size n is drawn from a...Ch. 5.2 - Let y1,y2,...,yn be a random sample of size n from...Ch. 5.2 - Prob. 18QCh. 5.2 - A criminologist is searching through FBI files to...Ch. 5.2 - Prob. 20QCh. 5.2 - Suppose that Y1=8.3,Y2=4.9,Y3=2.6, and Y4=6.5 is a...Ch. 5.2 - Find a formula for the method of moments estimate...Ch. 5.2 - Calculate the method of moments estimate for the...Ch. 5.2 - Find the method of moments estimates for and 2,...Ch. 5.2 - Use the method of moments to derive estimates for...Ch. 5.2 - Bird songs can be characterized by the number of...Ch. 5.2 - Prob. 27QCh. 5.3 - A commonly used IQ test is scaled to have a mean...Ch. 5.3 - The production of a nationally marketed detergent...Ch. 5.3 - Mercury pollution is widely recognized as a...Ch. 5.3 - A physician who has a group of thirty-eight female...Ch. 5.3 - Suppose a sample of size n is to be drawn from a...Ch. 5.3 - What confidence would be associated with each of...Ch. 5.3 - Five independent samples, each of size n, are to...Ch. 5.3 - Suppose that y1,y2,...,yn is a random sample of...Ch. 5.3 - If the standard deviation () associated with the...Ch. 5.3 - In 1927, the year he hit sixty home runs, Babe...Ch. 5.3 - A thirty-second commercial break during the...Ch. 5.3 - During one of the first beer wars in the early...Ch. 5.3 - The Pew Research Center did a survey of 2253...Ch. 5.3 - If (0.57,0.63) is a 50% confidence interval for p,...Ch. 5.3 - Suppose a coin is to be tossed n times for the...Ch. 5.3 - On the morning of November 9, 1994the day after...Ch. 5.3 - Which of the following two intervals has the...Ch. 5.3 - Prob. 18QCh. 5.3 - Prob. 19QCh. 5.3 - Prob. 20QCh. 5.3 - Prob. 21QCh. 5.3 - A public health official is planning for the...Ch. 5.3 - Prob. 23QCh. 5.3 - Given that a political poll shows that 52% of the...Ch. 5.3 - Prob. 25QCh. 5.3 - Suppose that p is to be estimated by Xn and we are...Ch. 5.3 - Let p denote the true proportion of college...Ch. 5.3 - Prob. 28QCh. 5.4 - Two chips are drawn without replacement from an...Ch. 5.4 - Suppose a random sample of size n=6 is drawn from...Ch. 5.4 - Prob. 3QCh. 5.4 - A sample of size n=16 is drawn from a normal...Ch. 5.4 - Suppose X1,X2,...,Xn is a random sample of size n...Ch. 5.4 - Prob. 6QCh. 5.4 - Let Y be the random variable described in Example...Ch. 5.4 - Suppose that 14, 10, 18, and 21 constitute a...Ch. 5.4 - A random sample of size 2, Y1 and Y2, is drawn...Ch. 5.4 - A sample of size 1 is drawn from the uniform pdf...Ch. 5.4 - Suppose that W is an unbiased estimator for . Can...Ch. 5.4 - We showed in Example 5.4.4 that 2=1ni=1n(YiY)2 is...Ch. 5.4 - As an alternative to imposing unbiasedness, an...Ch. 5.4 - Let Y1,Y2,...,Yn be a random sample of size n from...Ch. 5.4 - An estimator n=h(W1,...,Wn) is said to be...Ch. 5.4 - Is the maximum likelihood estimator for 2 in a...Ch. 5.4 - Let X1,X2,...,Xn denote the outcomes of a series...Ch. 5.4 - Suppose that n=5 observations are taken from the...Ch. 5.4 - Let Y1,Y2,...,Yn be a random sample of size n from...Ch. 5.4 - Given a random sample of size n from a Poisson...Ch. 5.4 - If Y1,Y2,...,Yn are random observations from a...Ch. 5.4 - Suppose that W1 is a random variable with mean ...Ch. 5.5 - Let Y1,Y2,...,Yn be a random sample from...Ch. 5.5 - Let X1,X2,...,Xn be a random sample of size n from...Ch. 5.5 - Suppose a random sample of size n is taken from a...Ch. 5.5 - Let Y1,Y2,...,Yn be a random sample from the...Ch. 5.5 - Prob. 5QCh. 5.5 - Let Y1,Y2,...,Yn be a random sample of size n from...Ch. 5.5 - Prove the equivalence of the two forms given for...Ch. 5.6 - Let X1,X2,...,Xn be a random sample of size n from...Ch. 5.6 - Let X1,X2, and X3 be a set of three independent...Ch. 5.6 - If is sufficient for , show that any one-to-one...Ch. 5.6 - Show that 2=i=1nYi2 is sufficient for 2 if...Ch. 5.6 - Let Y1,Y2,...,Yn be a random sample of size n from...Ch. 5.6 - Let Y1,Y2,...,Yn be a random sample of size n from...Ch. 5.6 - Suppose a random sample of size n is drawn from...Ch. 5.6 - Suppose a random sample of size n is drawn from...Ch. 5.6 - Prob. 9QCh. 5.6 - Prob. 10QCh. 5.6 - Prob. 11QCh. 5.7 - How large a sample must be taken from a normal pdf...Ch. 5.7 - Let Y1,Y2,...,Yn be a random sample of size n from...Ch. 5.7 - Suppose Y1,Y2,...,Yn is a random sample from the...Ch. 5.7 - An estimator n is said to be squared-error...Ch. 5.7 - Suppose n=Ymax is to be used as an estimator for...Ch. 5.7 - Prob. 6QCh. 5.8 - Prob. 1QCh. 5.8 - Find the squared-error loss [L(,)=()2] Bayes...Ch. 5.8 - Prob. 3QCh. 5.8 - Prob. 4QCh. 5.8 - Prob. 5QCh. 5.8 - Suppose that Y is a gamma random variable with...Ch. 5.8 - Prob. 7QCh. 5.8 - Find the squared-error loss Bayes estimate for in...Ch. 5.8 - Prob. 9Q
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- To help consumers in purchasing a laptop computer, Consumer Reports calculates an overall test score for each computer tested based upon rating factors such as ergonomics, portability, performance, display, and battery life. Higher overall scores indicate better test results. The following data show the average retail price and the overall score for ten 13-inch models (Consumer Reports website, October 25, 2012). Brand & Model Price ($) Overall Score Samsung Ultrabook NP900X3C-A01US 1250 83 Apple MacBook Air MC965LL/A 1300 83 Apple MacBook Air MD231LL/A 1200 82 HP ENVY 13-2050nr Spectre XT 950 79 Sony VAIO SVS13112FXB 800 77 Acer Aspire S5-391-9880 Ultrabook 1200 74 Apple MacBook Pro MD101LL/A 1200 74 Apple MacBook Pro MD313LL/A 1000 73 Dell Inspiron I13Z-6591SLV 700 67 Samsung NP535U3C-A01US 600 63 a. Select a scatter diagram with price as the independent variable. b. What does the scatter diagram developed in part (a) indicate about the relationship…arrow_forwardTo the Internal Revenue Service, the reasonableness of total itemized deductions depends on the taxpayer’s adjusted gross income. Large deductions, which include charity and medical deductions, are more reasonable for taxpayers with large adjusted gross incomes. If a taxpayer claims larger than average itemized deductions for a given level of income, the chances of an IRS audit are increased. Data (in thousands of dollars) on adjusted gross income and the average or reasonable amount of itemized deductions follow. Adjusted Gross Income ($1000s) Reasonable Amount ofItemized Deductions ($1000s) 22 9.6 27 9.6 32 10.1 48 11.1 65 13.5 85 17.7 120 25.5 Compute b1 and b0 (to 4 decimals).b1 b0 Complete the estimated regression equation (to 2 decimals). = + x Predict a reasonable level of total itemized deductions for a taxpayer with an adjusted gross income of $52.5 thousand (to 2 decimals). thousand dollarsWhat is the value, in dollars, of…arrow_forwardK The mean height of women in a country (ages 20-29) is 63.7 inches. A random sample of 65 women in this age group is selected. What is the probability that the mean height for the sample is greater than 64 inches? Assume σ = 2.68. The probability that the mean height for the sample is greater than 64 inches is (Round to four decimal places as needed.)arrow_forward
- In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 69.6 inches and a standard deviation of 4.0 inches. A study participant is randomly selected. Complete parts (a) through (d) below. (a) Find the probability that a study participant has a height that is less than 68 inches. The probability that the study participant selected at random is less than 68 inches tall is 0.4. (Round to four decimal places as needed.) 20 2arrow_forwardPEER 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?arrow_forwardQuestions 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.arrow_forward
- You are provided with data that includes all 50 states of the United States. Your task is to draw a sample of: o 20 States using Random Sampling (2 points: 1 for random number generation; 1 for random sample) o 10 States using Systematic Sampling (4 points: 1 for random numbers generation; 1 for random sample different from the previous answer; 1 for correct K value calculation table; 1 for correct sample drawn by using systematic sampling) (For systematic sampling, do not use the original data directly. Instead, first randomize the data, and then use the randomized dataset to draw your sample. Furthermore, do not use the random list previously generated, instead, generate a new random sample for this part. For more details, please see the snapshot provided at the end.) Upload a Microsoft Excel file with two separate sheets. One sheet provides random sampling while the other provides systematic sampling. Excel snapshots that can help you in organizing columns are provided on the next…arrow_forwardThe population mean and standard deviation are given below. Find the required probability and determine whether the given sample mean would be considered unusual. For a sample of n = 65, find the probability of a sample mean being greater than 225 if μ = 224 and σ = 3.5. For a sample of n = 65, the probability of a sample mean being greater than 225 if μ=224 and σ = 3.5 is 0.0102 (Round to four decimal places as needed.)arrow_forward***Please do not just simply copy and paste the other solution for this problem posted on bartleby as that solution does not have all of the parts completed for this problem. Please answer this I will leave a like on the problem. The data needed to answer this question is given in the following link (file is on view only so if you would like to make a copy to make it easier for yourself feel free to do so) https://docs.google.com/spreadsheets/d/1aV5rsxdNjHnkeTkm5VqHzBXZgW-Ptbs3vqwk0SYiQPo/edit?usp=sharingarrow_forward
- The data needed to answer this question is given in the following link (file is on view only so if you would like to make a copy to make it easier for yourself feel free to do so) https://docs.google.com/spreadsheets/d/1aV5rsxdNjHnkeTkm5VqHzBXZgW-Ptbs3vqwk0SYiQPo/edit?usp=sharingarrow_forwardThe following relates to Problems 4 and 5. Christchurch, New Zealand experienced a major earthquake on February 22, 2011. It destroyed 100,000 homes. Data were collected on a sample of 300 damaged homes. These data are saved in the file called CIEG315 Homework 4 data.xlsx, which is available on Canvas under Files. A subset of the data is shown in the accompanying table. Two of the variables are qualitative in nature: Wall construction and roof construction. Two of the variables are quantitative: (1) Peak ground acceleration (PGA), a measure of the intensity of ground shaking that the home experienced in the earthquake (in units of acceleration of gravity, g); (2) Damage, which indicates the amount of damage experienced in the earthquake in New Zealand dollars; and (3) Building value, the pre-earthquake value of the home in New Zealand dollars. PGA (g) Damage (NZ$) Building Value (NZ$) Wall Construction Roof Construction Property ID 1 0.645 2 0.101 141,416 2,826 253,000 B 305,000 B T 3…arrow_forwardRose Par posted Apr 5, 2025 9:01 PM Subscribe To: Store Owner From: Rose Par, Manager Subject: Decision About Selling Custom Flower Bouquets Date: April 5, 2025 Our shop, which prides itself on selling handmade gifts and cultural items, has recently received inquiries from customers about the availability of fresh flower bouquets for special occasions. This has prompted me to consider whether we should introduce custom flower bouquets in our shop. We need to decide whether to start offering this new product. There are three options: provide a complete selection of custom bouquets for events like birthdays and anniversaries, start small with just a few ready-made flower arrangements, or do not add flowers. There are also three possible outcomes. First, we might see high demand, and the bouquets could sell quickly. Second, we might have medium demand, with a few sold each week. Third, there might be low demand, and the flowers may not sell well, possibly going to waste. These outcomes…arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781337278461
Author:Ron Larson
Publisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Functions and Change: A Modeling Approach to Coll...
Algebra
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Cengage Learning
Finding Local Maxima and Minima by Differentiation; Author: Professor Dave Explains;https://www.youtube.com/watch?v=pvLj1s7SOtk;License: Standard YouTube License, CC-BY