UNIVERSITY of TORONTO. Faculty of Arts and Science


 Frederica Kelly
 2 years ago
 Views:
Transcription
1 UNIVERSITY of TORONTO Faculty of Arts and Science AUGUST 2005 EXAMINATION AT245HS uration  3 hours Examination Aids: Nonprogrammable or SOAapproved calculator. Instruction:. There are 27 equally weighted questions on 8 pages. Please check if you have all the pages before proceeding. 2. o not spend too much time on one single question. Page of
2 . 2. A An insurance company estimates that 40% of policyholders who have only an auto policy will renew next year and 60% of policyholders who have only a homeowners policy will renew next year. The company estimates that 80% of policyholders who have both an auto and a homeowner s policy will renew at least one of those policies next year. ompany records shows that 65% of policyholders have an auto policy, 50% of policyholders have a homeowner s policy, and 5% of policyholders have both an auto and a homeowner s policy. Using the company s estimates, calculate the percentage of policyholders that will renew at least one policy next year. A) 20 B) 29 ) 4 ) 53 E) 70 An insurance company examines its pool of auto insurance customers and gathers the following information: i. All customers insure at least one car ii. 64% of the customers insure more than one car iii. 20% of the customers insure a sports car iv. Of those who insure more than one car, 5% insure a sports car. What is the probability that a randomly selected customer insures exactly one car, and the car is a sport car? A) 0.0 B) 0.02 ) 0.03 ) 0.04 E) None is correct An insurer offers a health plan to the employees of a large company. As part of this plan, the individual employees may choose exactly two of the supplementary coverages, A, B, and, or they may choose no supplementary coverage. The proportions of the company s employees that choose coverages A, B and are 4, 3, and 5 2, respectively. etermine the probability that a randomly chosen employee will choose no supplementary coverage. A) 0 B) ) 2 ) E) 7 9 An insurance company pays hospital claims. The number of claims that include emergency room or operating room charges is 85% of the total number of claims. The Page 2 of 2
3 5. 6. B 7. number of claims that do not include emergency room charges is 25% of the total number of claims. The occurrence of emergency room charges is independent of the occurrence of operating room charges no hospital claims. alculate the probability that a claim submitted to the insurance company includes operating room charges. A) 0.0 B) 0.20 ) 0.25 ) 0.40 E) 0.80 An insurance company issues life insurance policies in three separate categories: standard, preferred, and ultrapreferred. Of the company s policyholders, 50% are standard, 40% are preferred, and 0% are ultrapreferred. Each standard policyholder has probability 0.0 of dying in the next year, each preferred policyholder has probability of dying in the next year, and each ultrapreferred policyholder has probability 0.00 of dying in the next year. A policyholder dies in the next year. What is the probability that the deceased policyholder was ultrapreferred? A) B) 0.00 ) ) 0.04 E) Upon arrival at a hospital s emergency room, patients are categorized according to their condition as critical, serious, or stable. In the past year: i. 0% of the emergency room patients were critical; ii. 30% of the emergency room patients were serious; iii. the rest of the emergency room patients were stable; iv. 40% of the critical patients died v. 0% of the serious patients died; vi. % of the stable patients died. Given that a patient survived, what is the probability that the patient was categorized as serious upon arrival? A) 0.06 B) 0.29 ) 0.30 ) 0.39 E) 0.64 The number of days that elapse between the beginning of a calendar year and the moment a highrisk driver is involved in an accident is exponentially distributed. An insurance company expects that 30% of highrisk drivers will be involved in an accident during the first 50 days of a calendar year. What portion of highrisk drivers is expected to be involved in an accident during the first Page 3 of 3
4 E days of a calendar year? A) 0.53 B) ) ) E) A large pool of adults earning their first driver s license includes 50% lowrisk drivers, 30% moderaterisk drivers, and 20% highrisk drivers. Because these drivers have no prior driving record, an insurance company considers each driver to be randomly selected form the pool. This month, the insurance company writes 4 new policies for adults earning their first driver s license. What is the probability that these 4 will contain at least two more highrisk drivers than lowrisk drivers? A) B) 0.02 ) 0.08 ) E) The lifetime of a machine part has a continuous distribution on the interval (0, 40) with probability density function f, where f(x) is proportional to (0 + x) 2. What is the probability that the lifetime of the machine part is less than 5? A) 0.03 B) 0.3 ) 0.42 ) 0.58 E) 0.97 A study is being conducted in which the health of two independent groups of ten policyholders is being monitored over a oneyear period of time. Individual participants in the study drop out before the end of the study with probability 0.2 independently of the other participants. What is the probability that at least 9 participants complete the study in one of the two groups, but not in both groups? A) B) 0.92 ) ) E) Let X be a continuous random variable with density function alculate the expected value of X. A) 5 B) x 2 x 4 f (x) = 0 0 otherwise 3 5 ) ) 28 5 E) 2 5 A device that continuously measures and records seismic activities is placed in a remote region. The time, T, to failure of this device is exponentially distributed with mean 3 years. Since the device will not be monitored during its first two years of service, the time Page 4 of 4
5 to discovery of its failure is X = max(t, 2). etermine the expected value of X. A) e6 B) 2 2e e ) 3 3 ) 2 + 3e E) 5 3. A 4. A probability distribution of the claim sizes for an auto insurance policy is given in the table below: laim Size Probability What percentage of the claims is within one standard deviation of the mean claim size? A) 45% B) 55% ) 68% ) 85% E) 00% A company agrees to accept the highest of four sealed bids on a property. The four bids are regards as four independent random variables with common cumulative distribution function: F(x) = 2 ( + sin x) 3 2 x Which of the following represents the expected value of the accepted bid? A) B) ) ) E) x cos xdx 6 ( + sin x)4 dx 6 x( + sin x) 4 dx 4 x cos x( + sin x)3 dx 4 cos x( + sin x)3 dx 5. E An investment accounts earns an annual interest rate R that follows a uniform distribution on the interval (0.04, 0.08). The value of a 0,000 initial investment in this account after one year is given by V = 0,000e R. etermine the cumulative distribution function F(v) of V for values of v satisfying 0 < F(v) <. A) 0000ev/ B) 25e v/ ) v ) 25 v v E) 25 ln Let T denote the time in minutes for a customer service representative to respond to 0 Page 5 of 5
6 E telephone inquires. T is uniformly distributed on the interval with endpoints 8 and 2 minutes. Let R denote the average rate, in customers per minute, at which the representative responds to inquiries. 7. A Which of the following is the density function of the random variable R on the interval 0 2,0 8 A) 2 5 B) 3 r ) 3r 5ln(r) 2 ) 0 r 2 E) 5 2r 2 laim amounts for wind damage to insured homes are independent random variables with common density function: 3 x > f (x) = x 4, where x is the amount of a claim in thousands. 0 otherwise Suppose 3 such claims will be made. What is the expected value of the largest of the three claims? A) 2,025 B) 2,700 ) 3,232 ) 3,375 E) 4, xy 0 x, x y 2x E f (x, y) = 3 0 otherwise alculate the conditional expectation of Y, given X = 0.5 A) 2 B) 2 3 ) 3 4 ) 5 7 E) For a group of car insurance policies, a loss X is assumed to be a random variable whose distribution follows the density function: f (x) = 8,000,000 x > 0 (x + 2,000) 3 If no deductible amount is applied to a loss, the expected number of claims paid in the next year is 2,500. alculate the deductible amount d to be applied to each loss that would reduce the expected NUMBER of losses in the next year by 36%. A) 00 B) 250 ) 400 ) 500 E),000 Page 6 of 6
7 E 24. B For claims involving two cars, an auto insurance policy will pay for the damage to both the policyholder s car and the other car involved in a collision, if the policyholder is responsible. The damage (in thousands) to the policyholder s car, X, is uniformly distributed on the interval [, 4]. Given that X = k, the damage to the other car follows a uniform distribution on the interval [k 0.5, k + 2.5]. alculate the expected total cost to the insurer for an accident that is the responsibility of one of their policyholders. A) 5.0 B) 5.5 ) 6.0 ) 6.5 E) 7.0 The owner of a car purchases insurance against collision damage to his vehicle. If a collision occurs, the repair cost is uniformly distributed on the interval [500, 5000]. The policy limits repair reimbursements up to 2,500 per collision. Given that a collision occurs, calculate the mean plus two standard deviations for the insurance reimbursement. A) 2,056 B) 2,650 ) 3,33 ) 3,478 E) 3,652 Let X and Y denote the values of two stocks at the end of a fiveyear period. X is uniformly distributed on the interval (0, 2). Given X = k, Y is uniformly distributed on the interval (0, k). etermine covariance of X and Y according to this model. A) 0 B) 4 ) 6 ) 2 E) 24 The time (in days) until failure of a certain electronic device follows the probability density function: f (t) = 20, where t > 20 and >. t + alculate the probability that the device will fail within 30 days if the mean failure time is 30 days. A) B) ) ) E) A model for the lifetime of a new small business gives the probability of failure in the n th month as n for n =, 2, 3,. etermine the largest number of whole months after which there is at least a 5% chance that a new small business will still be operating. A) 2 B) 3 ) 4 ) 5 E) 6 Page 7 of 7
8 25. B B Let X and Y be continuous random variables with joint density function: f (x, y) = 5y x2 y x 0 otherwise alculate Pr(Y 0.25) A) 0.0 B) 0. ) 0.2 ) 0.3 E) 0.4 An insurance policy reimburses a loss up to a benefit limit of 0. The policyholder s loss X follows a distribution with density function: 2 x > f (x) = x 3 0 otherwise What is the expected value of the BENEFIT paid under this insurance policy? A).0 B).3 ).8 ).9 E) 2.0 An actuary determines that the claim size for a certain class of accidents is a random variable X with moment generating function: M X (t) = ( 2500t) 4 etermine the standard deviation for the claim size for this class of accident. A),340 B) 5,000 ) 8,660 ) 0,000 E),80 Page 8 of 8
Math 370, Spring 2008 Prof. A.J. Hildebrand. Practice Test 2
Math 370, Spring 2008 Prof. A.J. Hildebrand Practice Test 2 About this test. This is a practice test made up of a random collection of 15 problems from past Course 1/P actuarial exams. Most of the problems
More information1. A survey of a group s viewing habits over the last year revealed the following
1. A survey of a group s viewing habits over the last year revealed the following information: (i) 8% watched gymnastics (ii) 9% watched baseball (iii) 19% watched soccer (iv) 14% watched gymnastics and
More informationSOCIETY OF ACTUARIES/CASUALTY ACTUARIAL SOCIETY EXAM P PROBABILITY EXAM P SAMPLE QUESTIONS
SOCIETY OF ACTUARIES/CASUALTY ACTUARIAL SOCIETY EXAM P PROBABILITY EXAM P SAMPLE QUESTIONS Copyright 005 by the Society of Actuaries and the Casualty Actuarial Society Some of the questions in this study
More informationSOCIETY OF ACTUARIES/CASUALTY ACTUARIAL SOCIETY EXAM P PROBABILITY EXAM P SAMPLE QUESTIONS
SOCIETY OF ACTUARIES/CASUALTY ACTUARIAL SOCIETY EXAM P PROBABILITY EXAM P SAMPLE QUESTIONS Copyright 007 by the Society of Actuaries and the Casualty Actuarial Society Some of the questions in this study
More informationSOCIETY OF ACTUARIES EXAM P PROBABILITY EXAM P SAMPLE QUESTIONS
SOCIETY OF ACTUARIES EXAM P PROBABILITY EXAM P SAMPLE QUESTIONS Copyright 015 by the Society of Actuaries Some of the questions in this study note are taken from past examinations. Some of the questions
More informationMath 370/408, Spring 2008 Prof. A.J. Hildebrand. Actuarial Exam Practice Problem Set 1
Math 370/408, Spring 2008 Prof. A.J. Hildebrand Actuarial Exam Practice Problem Set 1 About this problem set: These are problems from Course 1/P actuarial exams that I have collected over the years, grouped
More informationMath 370/408, Spring 2008 Prof. A.J. Hildebrand. Actuarial Exam Practice Problem Set 3 Solutions
Math 37/48, Spring 28 Prof. A.J. Hildebrand Actuarial Exam Practice Problem Set 3 Solutions About this problem set: These are problems from Course /P actuarial exams that I have collected over the years,
More informationMath 370, Spring 2008 Prof. A.J. Hildebrand. Practice Test 2 Solutions
Math 370, Spring 008 Prof. A.J. Hildebrand Practice Test Solutions About this test. This is a practice test made up of a random collection of 5 problems from past Course /P actuarial exams. Most of the
More informationSOCIETY OF ACTUARIES/CASUALTY ACTUARIAL SOCIETY EXAM P PROBABILITY EXAM P SAMPLE QUESTIONS
SOCIETY OF ACTUARIES/CASUALTY ACTUARIAL SOCIETY EXAM P PROBABILITY EXAM P SAMPLE QUESTIONS Copyright 5 by the Society of Actuaries and the Casualty Actuarial Society Some of the questions in this study
More informationMath 370, Actuarial Problemsolving Spring 2008 A.J. Hildebrand. Problem Set 1 (with solutions)
Math 370, Actuarial Problemsolving Spring 2008 A.J. Hildebrand Problem Set 1 (with solutions) About this problem set: These are problems from Course 1/P actuarial exams that I have collected over the years,
More informationHomework 3 Solution, due July 16
Homework 3 Solution, due July 16 Problems from old actuarial exams are marked by a star. Problem 1*. Upon arrival at a hospital emergency room, patients are categorized according to their condition as
More informationMath 370, Actuarial Problemsolving Spring 2008 A.J. Hildebrand. Practice Test, 1/28/2008 (with solutions)
Math 370, Actuarial Problemsolving Spring 008 A.J. Hildebrand Practice Test, 1/8/008 (with solutions) About this test. This is a practice test made up of a random collection of 0 problems from past Course
More informationMath 370, Spring 2008 Prof. A.J. Hildebrand. Practice Test 1 Solutions
Math 70, Spring 008 Prof. A.J. Hildebrand Practice Test Solutions About this test. This is a practice test made up of a random collection of 5 problems from past Course /P actuarial exams. Most of the
More informationSTA 256: Statistics and Probability I
Al Nosedal. University of Toronto. Fall 2014 1 2 3 4 5 My momma always said: Life was like a box of chocolates. You never know what you re gonna get. Forrest Gump. Experiment, outcome, sample space, and
More informationJoint Exam 1/P Sample Exam 1
Joint Exam 1/P Sample Exam 1 Take this practice exam under strict exam conditions: Set a timer for 3 hours; Do not stop the timer for restroom breaks; Do not look at your notes. If you believe a question
More informationEDUCATION AND EXAMINATION COMMITTEE SOCIETY OF ACTUARIES RISK AND INSURANCE. Copyright 2005 by the Society of Actuaries
EDUCATION AND EXAMINATION COMMITTEE OF THE SOCIET OF ACTUARIES RISK AND INSURANCE by Judy Feldman Anderson, FSA and Robert L. Brown, FSA Copyright 25 by the Society of Actuaries The Education and Examination
More informationCOURSE 1 REVISED SAMPLE EXAM
COURSE REVISED SAMPLE EXAM A table of values for the normal distribution will be provided with the Course Exam. Revised August 999 Problem # A marketing survey indicates that 60% of the population owns
More informationCHAPTER 28 Insurance
CHAPTER 28 Insurance Chapter Objectives After studying this chapter, you will be able to describe types of automobile insurance coverage. explain the importance of health insurance as a fringe benefit
More informationMathematics of Risk. Introduction. Case Study #1 Personal Auto Insurance Pricing. Mathematical Concepts Illustrated. Background
Mathematics of Risk Introduction There are many mechanisms that individuals and organizations use to protect themselves against the risk of financial loss. Government organizations and public and private
More information3. The Economics of Insurance
3. The Economics of Insurance Insurance is designed to protect against serious financial reversals that result from random evens intruding on the plan of individuals. Limitations on Insurance Protection
More informationPLYMOUTH ROCK ASSURANCE CORPORATION. Extended Coverages for Motor Club Members
PLYMOUTH ROCK ASSURANCE CORPORATION Extended Coverages for Motor Club Members The benefits and enhancements provided by this endorsement are available only to policies issued to members in good standing
More informationMath 370/408, Spring 2008 Prof. A.J. Hildebrand. Actuarial Exam Practice Problem Set 5 Solutions
Math 370/408, Spring 2008 Prof. A.J. Hildebrand Actuarial Exam Practice Problem Set 5 Solutions About this problem set: These are problems from Course 1/P actuarial exams that I have collected over the
More information( ) is proportional to ( 10 + x)!2. Calculate the
PRACTICE EXAMINATION NUMBER 6. An insurance company eamines its pool of auto insurance customers and gathers the following information: i) All customers insure at least one car. ii) 64 of the customers
More informationManaging Risk: The Good News About Insurance
THEME 5 MONEY MANAGEMENT LESSON 22 Managing Risk: The Good News About Insurance Fitness Focus EQUIPMENT AND GETTING READY! Exercise 22.1, Choices and Risks (Bringing Home the Gold Student Workouts) Exercise
More informationCHAPTER 6: Continuous Uniform Distribution: 6.1. Definition: The density function of the continuous random variable X on the interval [A, B] is.
Some Continuous Probability Distributions CHAPTER 6: Continuous Uniform Distribution: 6. Definition: The density function of the continuous random variable X on the interval [A, B] is B A A x B f(x; A,
More informationNovember 2012 Course MLC Examination, Problem No. 1 For two lives, (80) and (90), with independent future lifetimes, you are given: k p 80+k
Solutions to the November 202 Course MLC Examination by Krzysztof Ostaszewski, http://www.krzysio.net, krzysio@krzysio.net Copyright 202 by Krzysztof Ostaszewski All rights reserved. No reproduction in
More information( ) = 1 x. ! 2x = 2. The region where that joint density is positive is indicated with dotted lines in the graph below. y = x
Errata for the ASM Study Manual for Exam P, Eleventh Edition By Dr. Krzysztof M. Ostaszewski, FSA, CERA, FSAS, CFA, MAAA Web site: http://www.krzysio.net Email: krzysio@krzysio.net Posted September 21,
More informationImportant Probability Distributions OPRE 6301
Important Probability Distributions OPRE 6301 Important Distributions... Certain probability distributions occur with such regularity in reallife applications that they have been given their own names.
More informationWe hope you will find this sample a useful supplement to your existing educational materials, and we look forward to receiving your comments.
To Teachers of Mathematics: Thank you for visiting the BeAnActuary.org booth at the annual meeting of the National Council of Teachers of Mathematics. BeAnActuary.org is sponsored by the Joint Career Encouragement
More informationSASKATCHEWAN PRESTIGE AUTO INSURANCE
Licence Plate Insurance... 2 Why Plate Insurance Isn t Enough... 3 Added Liability Protection... 4 Family Protection Coverage... 4 Vehicle Damage Deductible... 5 Accident Benefits... 5 NonOwned Driver
More informationEconomic Education for Consumers Chapter 14 Study Guide Automobile and Home Insurance: Sharing the Risk
Economic Education for Consumers Chapter 14 Study Guide Automobile and Home Insurance: Sharing the Risk Section 141 Insurance Basics Define Risk Management. Define Shared Risk. How do insurance companies
More informationMay 2012 Course MLC Examination, Problem No. 1 For a 2year select and ultimate mortality model, you are given:
Solutions to the May 2012 Course MLC Examination by Krzysztof Ostaszewski, http://www.krzysio.net, krzysio@krzysio.net Copyright 2012 by Krzysztof Ostaszewski All rights reserved. No reproduction in any
More informationMath 370/408, Spring 2008 Prof. A.J. Hildebrand. Actuarial Exam Practice Problem Set 2 Solutions
Math 70/408, Spring 2008 Prof. A.J. Hildebrand Actuarial Exam Practice Problem Set 2 Solutions About this problem set: These are problems from Course /P actuarial exams that I have collected over the years,
More informationInsurance Test  MoneyPower
Insurance Test  MoneyPower Multiple Choice Identify the choice that best completes the statement or answers the question. 1. For the past five years, a person has had a $20,000 whole life insurance policy
More informationSTAT 3502. x 0 < x < 1
Solution  Assignment # STAT 350 Total mark=100 1. A large industrial firm purchases several new word processors at the end of each year, the exact number depending on the frequency of repairs in the previous
More informationSASKATCHEWAN AUTO INSURANCE
Accident Benefits... 5 Added Liability Protection... 4 Affordable Premiums... 7 Coverage Summary Charts Commercial Vehicles... 9 Private Passenger Vehicles... 8 Family Protection Coverage... 4 Licence
More informationTexas Municipal Courts Education Center
TexasSure Bringing Insurance Verification Into the 21 st Century Texas Municipal Courts Education Center 20082009 Academic Year Session Learning Objectives: By the end of the session, participants should
More informationGEORGIA PERFORMANCE STANDARDS Personal Finance Domain
GEORGIA PERFORMANCE STANDARDS Personal Finance Domain Page 1 of 8 GEORGIA PERFORMANCE STANDARDS Personal Finance Concepts SSEPF1 The student will apply rational decision making to personal spending and
More informationChapter 10. Chapter 10 Learning Objectives. Insurance and Risk Management: An Introduction. Property and Motor Vehicle Insurance
Chapter 10 Property and Motor Vehicle Insurance McGrawHill/Irwin Copyright 2012 by The McGrawHill Companies, Inc. All rights reserved. 101 Chapter 10 Learning Objectives 1. Develop a risk management
More informationThe Game of Life Purchasing Auto Insurance Updated: 20160210
The Game of Life Purchasing Auto Insurance Updated: 20160210 One of the most common experiences young adults encounter can be one of the most mysterious: purchasing auto insurance. It might not seem
More informationA few tips to ensure that you claim correctly and receive your money as quickly as possible:
Car Insurance How can I keep my car insurance costs low? The first thing to do is bargain shop to make sure that the rates you are getting are reasonable in comparison to other companies. Within the policy
More informationManual for SOA Exam MLC.
Chapter 4. Life Insurance. Extract from: Arcones Manual for the SOA Exam MLC. Fall 2009 Edition. available at http://www.actexmadriver.com/ 1/14 Level benefit insurance in the continuous case In this chapter,
More informationINSURANCE BASICS (DON T RISK IT)
INSURANCE BASICS (DON T RISK IT) WHAT IS INSURANCE? Risk management tool that limits financial loss due to illness, injury or damage in exchange for a premium Shared Risk Insurance company collects premiums
More informationSmooth Sailing: Exploring Insurance and Estate Planning
Smooth Sailing: Exploring Insurance and Estate Planning LESSON 17: TEACHERS GUIDE Life isn t always smooth sailing, and if you re not prepared for bumpy waters, it can take a toll on your finances and
More informationNEW JERSEY AUTO INSURANCE, BUYER S GUIDE
NEW JERSEY AUTO INSURANCE, BUYER S GUIDE BGNJ (1/14) WHAT'S INSIDE WHEREDOISTART?...1 UNDERSTANDING YOUR POLICY...2 Types of Coverages Standard and Basic Policies What are Limits and Deductibles? UNDERSTANDING
More information5. Continuous Random Variables
5. Continuous Random Variables Continuous random variables can take any value in an interval. They are used to model physical characteristics such as time, length, position, etc. Examples (i) Let X be
More informationYour Guide to Auto Insurance Premiums
INSURANCE FACTS for Pennsylvania Consumers Your Guide to Auto Insurance Premiums 18778816388 Tollfree Automated Consumer Line www.insurance.state.pa.us Pennsylvnaia Insurance Department Website Required
More informationFREQUENTLY ASKED QUESTIONS
FREQUENTLY ASKED QUESTIONS What is TexasSure? GENERAL INFORMATION TexasSure is a new vehicle insurance verification system that will ultimately allow law enforcement and county tax officials to confirm
More informationGuide to Knowing Your Auto
Guide to Knowing Your Auto & Homeowners Insurance Options Presented by: 1 When it comes to insurance, you can never know too much. What type of insurance is available and how much coverage you need? And
More informationStudy Manual for Exam P/Exam 1. Probability
Study Manual for Exam P/Exam 1 Probability Eleventh Edition by Krzysztof Ostaszewski Ph.D., F.S.A., CFA, M.A.A.A. Note: NO RETURN IF OPENED TO OUR READERS: Please check A.S.M. s web site at www.studymanuals.com
More informationAuto, Homeowners, Medical and Life Insurance. Dollars and Sense
Auto, Homeowners, Medical and Life Insurance Dollars and Sense Copyright Copyright Texas Education Agency, 2014. These Materials are copyrighted and trademarked as the property of the Texas Education Agency
More informationAutomobile Insurance in Pennsylvania a supplement to the Automobile Insurance Guide
and answers about Automobile Insurance in Pennsylvania a supplement to the Automobile Insurance Guide My automobile policy was canceled because I did not pay my premium on time. Is this legal? Yes. If
More informationPoisson Processes. Chapter 5. 5.1 Exponential Distribution. The gamma function is defined by. Γ(α) = t α 1 e t dt, α > 0.
Chapter 5 Poisson Processes 5.1 Exponential Distribution The gamma function is defined by Γ(α) = t α 1 e t dt, α >. Theorem 5.1. The gamma function satisfies the following properties: (a) For each α >
More informationChapter 3 RANDOM VARIATE GENERATION
Chapter 3 RANDOM VARIATE GENERATION In order to do a Monte Carlo simulation either by hand or by computer, techniques must be developed for generating values of random variables having known distributions.
More informationCONSUMER S GUIDE TO AUTO INSURANCE
CONSUMER S GUIDE TO AUTO INSURANCE The Colorado Division of Insurance prepares this booklet to assist you in shopping for auto insurance and to help you understand your Personal Auto Policy. When shopping
More informationAutomobile Insurance 1
FCS7020 Automobile Insurance 1 Nayda I. Torres and Josephine Turner 2 An automobile is often the most expensive property that people own, next to a home. As a result, protection against loss of an automobile
More informationSOCIETY OF ACTUARIES. EXAM MLC Models for Life Contingencies EXAM MLC SAMPLE QUESTIONS
SOCIETY OF ACTUARIES EXAM MLC Models for Life Contingencies EXAM MLC SAMPLE QUESTIONS The following questions or solutions have been modified since this document was prepared to use with the syllabus effective
More informationStudy Manual for Exam P/Exam 1. Probability
Study Manual for Exam P/Exam 1 Probability Seventh Edition by Krzysztof Ostaszewski Ph.D., F.S.A., CFA, M.A.A.A. Note: NO RETURN IF OPENED TO OUR READERS: Please check A.S.M. s web site at www.studymanuals.com
More informationAllstate Indemnity Company Important Notice
Allstate Indemnity Company Important Notice Special Notice to Minnesota Auto Insureds The following surcharge information effective as of 8/2/2010 is provided to help you better understand your auto insurance
More informationWHERE TO GET MORE INFORMATION AND HELP
WHERE TO GET MORE INFORMATION AND HELP This Buyer's Guide is intended to provide general information to help you make coverage choices. It is not a substitute for the policy language, which governs. Additional
More informationNew Jersey Pre Signature Series to Signature Series Changes
Pre Signature Series Signature Series Key Differences AAA Loyal Member AAA Membership This discount is calculated based on the membership tenure of the policyholder provided they are an active member of
More informationLikelihood of Cancer
Suggested Grade Levels: 9 and up Likelihood of Cancer Possible Subject Area(s): Social Studies, Health, and Science Math Skills: reading and interpreting pie charts; calculating and understanding percentages
More informationUNIT I: RANDOM VARIABLES PART A TWO MARKS
UNIT I: RANDOM VARIABLES PART A TWO MARKS 1. Given the probability density function of a continuous random variable X as follows f(x) = 6x (1x) 0
More informationSolution. Let us write s for the policy year. Then the mortality rate during year s is q 30+s 1. q 30+s 1
Solutions to the May 213 Course MLC Examination by Krzysztof Ostaszewski, http://wwwkrzysionet, krzysio@krzysionet Copyright 213 by Krzysztof Ostaszewski All rights reserved No reproduction in any form
More informationMerchants Insurance Group New Hampshire Personal Lines Agents
March 16, 2011 BULLETIN NO. 5149NH TO: SUBJECT: Merchants Insurance Group New Hampshire Personal Lines Agents Introduction of Merchants Flexible Choice Auto sm Great News for Our Personal Lines Agents!
More informationNEW JERSEY AUTO INSURANCE BUYER S GUIDE *C00179480010000001* PL50074 (0312) Page 1 of 9 000001/00000 S1347I03 7668 07/23/12
NEW JERSEY AUTO INSURANCE BUYER S GUIDE *C00179480010000001* 000001/00000 S1347I03 7668 07/23/12 PL50074 (0312) Page 1 of 9 WHAT S INSIDE WHERE DO I START?... UNDERSTANDING YOUR POLICY... Types of Coverage
More informationTips To Save Money When Buying Insurance
Tips To Save Money When Buying Insurance This publication presents practical ideas for saving money on insurance. It is not intended to be an indepth source for insurance information, nor does it attempt
More informationNEW JERSEY AUTO SUPPLEMENT
AGENCY AGENCY CUSTOMER ID: NEW JERSEY AUTO SUPPLEMENT NAMED INSURED(S) POLICY NUMBER EFFECTIVE DATE CARRIER NAIC CODE NEW JERSEY AUTO INSURANCE BUYER'S GUIDE New Jersey Department of Banking and Insurance
More informationmade simple Personal Umbrella Policy Insurance What s inside:
Personal Umbrella Policy Insurance made simple What s inside: How to read an Allstate Personal Umbrella Policy Declarations Understanding personal umbrella policy insurance How to file a claim Frequently
More informationHierarchical Insurance Claims Modeling
Hierarchical Insurance Claims Modeling Edward W. (Jed) Frees, University of Wisconsin  Madison Emiliano A. Valdez, University of Connecticut 2009 Joint Statistical Meetings Session 587  Thu 8/6/0910:30
More informationUNIGARD INSURANCE COMPANY. Idaho PERSONAL UMBRELLA MANUAL
UNIGARD INSURANCE COMPANY Idaho PERSONAL UMBRELLA MANUAL Idaho Personal Lines Personal Umbrella i Application Binding Coverage Increased Limits Limits of Liability Introduction Policy Term Premium Determination
More information**BEGINNING OF EXAMINATION**
November 00 Course 3 Society of Actuaries **BEGINNING OF EXAMINATION**. You are given: R = S T µ x 0. 04, 0 < x < 40 0. 05, x > 40 Calculate e o 5: 5. (A) 4.0 (B) 4.4 (C) 4.8 (D) 5. (E) 5.6 Course 3: November
More informationTypes of Insurance Grade Level 912
1.10.1 Types of Insurance Grade Level 912 Take Charge of Your Finances Time to complete: 60 minutes National Content Standards Family and Consumer Science Standards: 1.1.6, 2.1.6, 2.5.4, 2.6.1, 2.6.3,
More informationNotes on Continuous Random Variables
Notes on Continuous Random Variables Continuous random variables are random quantities that are measured on a continuous scale. They can usually take on any value over some interval, which distinguishes
More informationMath 425 (Fall 08) Solutions Midterm 2 November 6, 2008
Math 425 (Fall 8) Solutions Midterm 2 November 6, 28 (5 pts) Compute E[X] and Var[X] for i) X a random variable that takes the values, 2, 3 with probabilities.2,.5,.3; ii) X a random variable with the
More informationAUTO. Insurance that keeps you moving
AUTO Insurance that keeps you moving Insurance in Motion Whether you own or lease, Kemper Preferred s insurance professionals have an auto policy that s right for you. Our rates are competitive, our service
More informationU.S Producer Price Index for Property and Casualty Insurance. Deanna Eggleston U.S. Bureau of Labor Statistics
U.S Producer Price Index for Property and Casualty Insurance Deanna Eggleston U.S. Bureau of Labor Statistics I. Industry Output The primary output of the property and casualty insurance industry is the
More informationAuto Insurance from The Hartford. Get the coverage and value you need for the long road ahead.
Auto Insurance from The Hartford Get the coverage and value you need for the long road ahead. Better coverage, better value for you and your family. When you buy auto insurance, you re not just protecting
More informationNEW JERSEY AUTO INSURANCE BUYER S GUIDE. Chris Christie Governor. Kim Guadagno Lt. Governor. Commissioner
NEW JERSEY AUTO INSURANCE BUYER S GUIDE Chris Christie Governor Kim Guadagno Lt. Governor Commissioner WHERE DO I START?... 1 UNDERSTANDING YOUR POLICY... 26 Types of Coverages Standard and Basic Policies
More informationNew Jersey AUTO INSURANCE
New Jersey AUTO INSURANCE Buyer s Guide Chris Christie Governor Kim Guadagno Lt. Governor Ken Kobylowski Commissioner NJM Insurance Group offers personal auto insurance in the voluntary market through
More information1. Let A, B and C are three events such that P(A) = 0.45, P(B) = 0.30, P(C) = 0.35,
1. Let A, B and C are three events such that PA =.4, PB =.3, PC =.3, P A B =.6, P A C =.6, P B C =., P A B C =.7. a Compute P A B, P A C, P B C. b Compute P A B C. c Compute the probability that exactly
More informationRE: Disclosure Requirements for Short Duration Insurance Contracts
INS14 November 21, 2014 Mr. Russell G. Golden Chairman Financial Accounting Standards Board 401 Merritt 7 P.O. Box 5116 Norwalk, Connecticut 068565116 RE: Disclosure Requirements for Short Duration Insurance
More informationNEW JERSEY AUTO INSURANCE
NEW JERSEY AUTO INSURANCE BUYER S GUIDE Chris Christie Governor Kim Guadagno Lt. Governor Richard J. Badolato Acting Commissioner NJM Insurance Group offers personal auto insurance in the voluntary market
More informationThe Distribution of Aggregate Life Insurance Claims
The Distribution of ggregate Life Insurance laims Tom Edwalds, FS Munich merican Reassurance o. BSTRT This paper demonstrates the calculation of the moments of the distribution of aggregate life insurance
More informationST 371 (VIII): Theory of Joint Distributions
ST 371 (VIII): Theory of Joint Distributions So far we have focused on probability distributions for single random variables. However, we are often interested in probability statements concerning two or
More informationMaster s Theory Exam Spring 2006
Spring 2006 This exam contains 7 questions. You should attempt them all. Each question is divided into parts to help lead you through the material. You should attempt to complete as much of each problem
More informationTHE CHALLENGE OF PRICING EXTENDED WARRANTIES. Author: Timothy L. Schilling
Title: THE CHALLENGE OF PRICING EXTENDED WARRANTIES Author: Timothy L. Schilling Biography: The author is a Consulting Actuary with Tillinghast, a Towers Perrin company. He is a Fellow of the Casualty
More informationJANUARY 2016 EXAMINATIONS. Life Insurance I
PAPER CODE NO. MATH 273 EXAMINER: Dr. C. BoadoPenas TEL.NO. 44026 DEPARTMENT: Mathematical Sciences JANUARY 2016 EXAMINATIONS Life Insurance I Time allowed: Two and a half hours INSTRUCTIONS TO CANDIDATES:
More informationJoint Probability Distributions and Random Samples. Week 5, 2011 Stat 4570/5570 Material from Devore s book (Ed 8), and Cengage
5 Joint Probability Distributions and Random Samples Week 5, 2011 Stat 4570/5570 Material from Devore s book (Ed 8), and Cengage Two Discrete Random Variables The probability mass function (pmf) of a single
More informationUNIVERSITY OF OSLO. The Poisson model is a common model for claim frequency.
UNIVERSITY OF OSLO Faculty of mathematics and natural sciences Candidate no Exam in: STK 4540 NonLife Insurance Mathematics Day of examination: December, 9th, 2015 Examination hours: 09:00 13:00 This
More informationEXAM 3, FALL 003 Please note: On a onetime basis, the CAS is releasing annotated solutions to Fall 003 Examination 3 as a study aid to candidates. It is anticipated that for future sittings, only the
More informationCHAPTER 7 SECTION 5: RANDOM VARIABLES AND DISCRETE PROBABILITY DISTRIBUTIONS
CHAPTER 7 SECTION 5: RANDOM VARIABLES AND DISCRETE PROBABILITY DISTRIBUTIONS TRUE/FALSE 235. The Poisson probability distribution is a continuous probability distribution. F 236. In a Poisson distribution,
More informationHome and Automobile Insurance Guide
Home and Automobile Insurance Guide General Information Finding the best insurance policies to suit your needs can be a complex and confusing business. To help you, we have addressed questions and defined
More informationExamination 110 Probability and Statistics Examination
Examination 0 Probability and Statistics Examination Sample Examination Questions The Probability and Statistics Examination consists of 5 multiplechoice test questions. The test is a threehour examination
More informationLecture 6: Discrete & Continuous Probability and Random Variables
Lecture 6: Discrete & Continuous Probability and Random Variables D. Alex Hughes Math Camp September 17, 2015 D. Alex Hughes (Math Camp) Lecture 6: Discrete & Continuous Probability and Random September
More informationTOP10 AUTO INSURANCE FAQ S
TOP10 AUTO INSURANCE FAQ S Lane s Insurance Chad answers the Top 10 most frequently asked Auto Insurance FAQ s A Publication By: 1 1  Why is my premium so high? Auto insurance premium rates are based
More informationWHITE PAPER Insurance Rates and Your Credit: What Every Consumer Should Know. October 21, 2013 1
WHITE PAPER Insurance Rates and Your Credit: What Every Consumer Should Know October 21, 2013 1 1. What is a CreditBased Insurance Score 2. Why do insurers use a CreditBased Insurance Score? 3. What
More informationChapter 22. Buying Insurance
Chapter 22 Buying Insurance Section 1 Insurance Basics I will be able to list some ways to lower insurance costs. The Language of Insurance 1. Insurance policy Policyholder 2. Insurance coverage Exclusions
More informationJointly Distributed Random Variables
Jointly Distributed Random Variables COMP 245 STATISTICS Dr N A Heard Contents 1 Jointly Distributed Random Variables 1 1.1 Definition......................................... 1 1.2 Joint cdfs..........................................
More information**BEGINNING OF EXAMINATION** The annual number of claims for an insured has probability function: , 0 < q < 1.
**BEGINNING OF EXAMINATION** 1. You are given: (i) The annual number of claims for an insured has probability function: 3 p x q q x x ( ) = ( 1 ) 3 x, x = 0,1,, 3 (ii) The prior density is π ( q) = q,
More information