Statistics (13th Edition)
13th Edition
ISBN: 9780134080215
Author: James T. McClave, Terry T Sincich
Publisher: PEARSON
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Chapter 4.3, Problem 40UP
To determine
Explain what the
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Could you please answer this question using excel.Thanks
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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.
Calculate the correlation coefficient r, letting Row 1 represent the x-values and Row 2 the y-values. Then calculate
it again, letting Row 2 represent the x-values and Row 1 the y-values. What effect does switching the variables have
on r?
Row 1
Row 2
13
149
25
36
41
60
62
78
S
205
122
195
173
133
197
24
Calculate the correlation coefficient r, letting Row 1 represent the x-values and Row 2 the y-values.
r=0.164 (Round to three decimal places as needed.)
S
24
Chapter 4 Solutions
Statistics (13th Edition)
Ch. 4.1 - What is a random variable?
Ch. 4.1 - How do discrete and continuous random variables...Ch. 4.1 - Type of Random Variable. Classify the following...Ch. 4.1 - Type of Random Variable. Identify the following...Ch. 4.1 - Type of Random Variable. Identify the following...Ch. 4.1 - 4.3 NHTSA crash tests. Refer to the National...Ch. 4.1 - 4.4 Customers in line at a Subway shop. The number...Ch. 4.1 - Sound waves from a basketball. Refer to the...Ch. 4.1 - Mongolian desert ants. Refer to the Journal of...Ch. 4.1 - Motivation of drug dealers. Refer to the Applied...
Ch. 4.1 - Psychology. Give an example of a discrete random...Ch. 4.1 - Sociology. Give an example of a discrete random...Ch. 4.1 - Nursing. Give an example of a discrete random...Ch. 4.1 - Art history. Give an example of a discrete random...Ch. 4.1 - Irrelevant speech effects. Refer to the Acoustical...Ch. 4.1 - Shaft graves in ancient Greece. Refer to the...Ch. 4.2 - Give three different ways of representing the...Ch. 4.2 - Consider the following probability...Ch. 4.2 - 4.11 A discrete random variable x can assume five...Ch. 4.2 - Explain why each of the following is or is not a...Ch. 4.2 - The random variable x has the following discrete...Ch. 4.2 - The random variable x has the discrete probability...Ch. 4.2 - 4.16 Toss three fair coins and let x equal the...Ch. 4.2 - Use the applet entitled Random Numbers to generate...Ch. 4.2 - Run the applet entitled Simulating the Probability...Ch. 4.2 - Size of TV households. According to Nielsen’s...Ch. 4.2 - 4.25 Do social robots walk or roll? Refer to the...Ch. 4.2 - NHTSA crash tests. Refer to the National Highway...Ch. 4.2 - Downloading apps to your cell phone. According to...Ch. 4.2 - Controlling the water hyacinth. An insect that...Ch. 4.2 - Gender in two-child families. Human Biology (Feb....Ch. 4.2 - Environmental vulnerability of amphibians. Many...Ch. 4.2 - The “last name” effect in purchasing. The Journal...Ch. 4.2 - Solar energy cells. According to the Earth Policy...Ch. 4.2 - 4.29 Contaminated gun cartridges. A weapons...Ch. 4.2 - Prob. 34ACICh. 4.2 - Prob. 35ACICh. 4.2 - Reliability of a manufacturing network. A team of...Ch. 4.2 - 4.38 Voter preferences for a committee. A...Ch. 4.2 - Prob. 38ACACh. 4.2 - Robot-sensor system configuration. Engineers at...Ch. 4.3 - What does the expected value of a random variable...Ch. 4.3 - Will E(x) always be equal to a specific value of...Ch. 4.3 - For a mound-shaped, symmetric distribution, what...Ch. 4.3 - Consider the probability distribution for the...Ch. 4.3 - 4.18 Consider the probability distribution for the...Ch. 4.3 - Consider the probability distributions shown...Ch. 4.3 - 4.17 Consider the probability distribution...Ch. 4.3 - NHTSA car crash tests. Refer to Exercise 4.26 (p....Ch. 4.3 - Downloading apps to your cell phone. Refer to the...Ch. 4.3 - Controlling the water hyacinth. Refer to the...Ch. 4.3 - Gender in two-child families. Refer to the Human...Ch. 4.3 - Environmental vulnerability of amphibians. Refer...Ch. 4.3 - Reliability of a manufacturing network. Refer to...Ch. 4.3 -
Beach erosional hot spots. Refer to the U.S....Ch. 4.3 - 4.36 Expected Lotto winnings. Most states offer...Ch. 4.3 -
Expected winnings in roulette. In the popular...Ch. 4.3 - 4.39 Parlay card betting. Odds makers try to...Ch. 4.4 - Give the five characteristics of a binomial random...Ch. 4.4 - Give the formula for p(x) for a binomial random...Ch. 4.4 - Consider the following binomial probability...Ch. 4.4 - Refer to Exercise 4.59.
Graph the probability...Ch. 4.4 - 4.40 Compute the following:
Ch. 4.4 - 4.42 Suppose x is a binomial random variable with...Ch. 4.4 - 4.43 If x is a binomial random variable, compute p...Ch. 4.4 - If x is a binomial random variable, use Table I in...Ch. 4.4 - If x is a binomial random variable, use Table I in...Ch. 4.4 - 4.45 If x is a binomial random variable, calculate...Ch. 4.4 - 4.46 The binomial probability distribution is a...Ch. 4.4 - Applet Exercise 4.3
Use the applets Simulating the...Ch. 4.4 - Applet Exercise 4.4
Open the applet Sample from a...Ch. 4.4 - Prob. 4.5AECh. 4.4 - Working on summer vacation. An Adweek/Harris (July...Ch. 4.4 - Superstitions survey. Are Americans superstitious?...Ch. 4.4 - Where will you get your next pet? According to an...Ch. 4.4 - Chemical signals of mice. Refer to the Cell (May...Ch. 4.4 - Analysis of bottled water. Is the bottled water...Ch. 4.4 - Caesarian births. The American College of...Ch. 4.4 - 4.53 Fingerprint expertise. Refer to the...Ch. 4.4 - Hotel guest satisfaction. J. D. Power and...Ch. 4.4 - 4.52 Immediate feedback to incorrect exam answers....Ch. 4.4 - 4.54 Making your vote count. Refer to the Chance...Ch. 4.4 - Prob. 78ACICh. 4.4 - Victims of domestic abuse. According to...Ch. 4.4 - Prob. 80ACICh. 4.4 - Testing a psychic’s ESP. Refer to Exercise 3.101...Ch. 4.4 - Assigning a passing grade. A literature professor...Ch. 4.4 - Prob. 83ACACh. 4.4 - Does having boys run in the family? Chance (Fall...Ch. 4.5 - Give the four characteristics of a Poisson random...Ch. 4.5 - Consider a Poisson random variable with...Ch. 4.5 - Consider the Poisson probability distribution...Ch. 4.5 - Refer to Exercise 4.86.
Graph the probability...Ch. 4.5 - Refer to Exercise 4.87.
Graph the probability...Ch. 4.5 - 4.65 Given that x is a random variable for which a...Ch. 4.5 - Assume that x is a random variable having a...Ch. 4.5 - Suppose x is a random variable for which a Poisson...Ch. 4.5 - Suppose x is a random variable for which a Poisson...Ch. 4.5 - As mentioned in this section, when n is large, p...Ch. 4.5 - Eye fixation experiment. Cognitive scientists at...Ch. 4.5 - Noise in laser imaging. Penumbrol imaging is a...Ch. 4.5 - Spare line replacement units. The U.S. Department...Ch. 4.5 - 4.176 NASA and rare planet transits. A “planet...Ch. 4.5 - 4.71 Airline fatalities. Over the past 5 years,...Ch. 4.5 - 4.76 Traffic fatalities and sporting events. The...Ch. 4.5 - LAN videoconferencing. A network administrator is...Ch. 4.5 - 4.80 Making high-stakes insurance decisions. The...Ch. 4.5 - Davy Crockett’s use of words. Davy Crockett, a...Ch. 4.5 - 4.79 Flaws in plastic-coated wire. The British...Ch. 4.5 - 4.82 Waiting for a car wash. An automatic car wash...Ch. 4.5 - 4.83 Elevator passenger arrivals. A study of the...Ch. 4.6 - Explain the difference between sampling with...Ch. 4.6 - Give the characteristics of a hypergeometric...Ch. 4.6 - How do binomial and hypergeometric random...Ch. 4.6 - 4.64 Given that x is a hypergeometric random...Ch. 4.6 - 4.63 Given that x is a hypergeometric random...Ch. 4.6 - Prob. 112LMCh. 4.6 - Prob. 113LMCh. 4.6 - 4.68 Given that x is a hypergeometric random...Ch. 4.6 - 4.67 Suppose you plan to sample 10 items from a...Ch. 4.6 - 4.69 Do social robots walk or roll? Refer to the...Ch. 4.6 - Mail rooms contaminated with anthrax. In Chance...Ch. 4.6 - Prob. 118ACBCh. 4.6 - 4.183 On-site treatment of hazardous waste. The...Ch. 4.6 - 4.78 Guilt in decision making. The Journal of...Ch. 4.6 - 4.73 Contaminated gun cartridges. Refer to the...Ch. 4.6 - Lot inspection sampling. Imagine that you are...Ch. 4.6 - Prob. 123ACICh. 4.6 - Prob. 124ACICh. 4.6 - Establishing boundaries in academic engineering....Ch. 4.6 - Prob. 126ACACh. 4.6 - Awarding of home improvement grants. The...Ch. 4 - Prob. 128UPCh. 4 - 4.161 Identify the type of random...Ch. 4 - 4.156 For each of the following examples, decide...Ch. 4 - Prob. 131LMCh. 4 - Prob. 132LMCh. 4 - Prob. 133LMCh. 4 - Prob. 134LMCh. 4 - Prob. 135LMCh. 4 - Prob. 136ACBCh. 4 - Prob. 137ACBCh. 4 - Prob. 138ACBCh. 4 - Prob. 139ACBCh. 4 - Prob. 140ACBCh. 4 - Prob. 141ACBCh. 4 - Prob. 142ACBCh. 4 - Prob. 143ACBCh. 4 - Prob. 144ACBCh. 4 - Prob. 145ACBCh. 4 - Prob. 146ACICh. 4 - Extinct New Zealand birds. Refer to the...Ch. 4 - Student gambling on sports. A study of gambling...Ch. 4 - Parents’ behavior at a gym meet. Pediatric...Ch. 4 - 4.196 Testing for spoiled wine. Suppose that you...Ch. 4 - Prob. 151ACICh. 4 - Prob. 152ACICh. 4 - Chickens with fecal contamination. The United...Ch. 4 - Crime Watch neighborhood. In many cities,...Ch. 4 - 4.203 The showcase showdown. On the popular...Ch. 4 - 4.60 Network forensic analysis. A network forensic...Ch. 4 - 4.201 How many questionnaires to mail? The...Ch. 4 - 4.204 Reliability of a “one-shot” device. A...Ch. 4 - Emergency room bed availability. The mean number...Ch. 4 - Prob. 160CTC
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