November 2000 Course 1Society of Actuaries/Casualty Actuarial SocietyNovember 20001Course 11.A recent study indicates that the annual cost of maintaining and repairing a car in a townin Ontario averages 200 with a variance of 260 .If a tax of 20% is introduced on all items associated with the maintenance and repair ofcars (i.e., everything is made 20% more expensive), what will be the variance of theannual cost of maintaining and repairing a car?(A)208(B)260(C)270(D)312(E)374Course 12Form 00B2.An investor purchases two assets, each having an initial value of 1000 . The value Vnof the first asset after n years can be modeled by the relationship:Vn = 1.10Vn1 for n = 1, 2, 3, . . .The value Wn of the second asset after n years can be modeled by the relationship:Wn = Wn1 + 0.20W0 for n = 1, 2, 3, . . .According to these models, by how much will the value of the first asset exceed the valueof the second asset after 25 years?(A) 4050(B) 4835(C) 5035(D) 5718(E) 6000November 20003Course 13.An auto insurance company has 10,000 policyholders. Each policyholder is classified as(i)young or old;(ii)male or female; and(iii)married or single.Of these policyholders, 3000 are young, 4600 are male, and 7000 are married. Thepolicyholders can also be classified as 1320 young males, 3010 married males, and1400 young married persons. Finally, 600 of the policyholders are young marriedmales.How many of the companys policyholders are young, female, and single?(A)280(B) 423(C) 486(D)880(E) 896Course 14Form 00B4.A diagnostic test for the presence of a disease has two possible outcomes: 1 for diseasepresent and 0 for disease not present. Let X denote the disease state of a patient, and let Ydenote the outcome of the diagnostic test. The joint probability function of X and Y isgiven by:P(X = 0, Y = 0) = 0.800P(X = 1, Y = 0) = 0.050P(X = 0, Y = 1) = 0.025P(X = 1, Y = 1) = 0.125Calculate Var(1)Y X = .(A)0.13(B)0.15(C)0.20(D)0.51(E)0.71November 20005Course 15.An equation of the line tangent to the graph of a differentiable function f at x = 0is y = 3x + 4 .Determine 0( )limsin(2 )xx f x x.(A)0(B)1(C)2(D)4(E)The limit does not exist.Course 16Form 00B6.An insurance company issues 1250 vision care insurance policies. The number of claimsfiled by a policyholder under a vision care insurance policy during one year is a Poissonrandom variable with mean 2 . Assume the numbers of claims filed by distinctpolicyholders are independent of one another.What is the approximate probability that there is a total of between 2450 and 2600 claimsduring a one-year period?(A)0.68(B)0.82(C)0.87(D)0.95(E)1.00November 20007Course 17.A group insurance policy covers the medical claims of the employees of a smallcompany. The value, V, of the claims made in one year is described byV = 100,000Ywhere Y is a random variable with density function4(1)for 01( )0otherwise, kyyf y Var(Y) and Var(X + Y) Var(X) + Var(Y) .(B)Var(X) Var(Y) and Var(X + Y) Var(Y) and Var(X + Y) = Var(X) + Var(Y) .(D)Var(X) Var(X) + Var(Y) .(E)Var(X) f(x2, y2), wheref(x,y) = x0.75y 0.25 for x, y 0 .What is the maximum value of f(x,y) that can be achieved given the consumersspending constraint?(A) 6.78(B) 7.50(C) 8.41(D) 9.58(E)11.40Course 122Form 00B22.The probability that a randomly chosen male has a circulation problem is 0.25 . Maleswho have a circulation problem are twice as likely to be smokers as those who do nothave a circulation problem.What is the conditional probability that a male has a circulation problem, given that he isa smoker?(A)1 4(B)1 3(C)2 5(D)1 2(E)2 3November 200023Course 123.A company buys a policy to insure its revenue in the event of major snowstorms that shutdown business. The policy pays nothing for the first such snowstorm of the year and10,000 for each one thereafter, until the end of the year. The number of majorsnowstorms per year that shut down business is assumed to have a Poisson distributionwith mean 1.5 .What is the expected amount paid to the company under this policy during a one-yearperiod?(A) 2,769(B) 5,000(C) 7,231(D) 8,347(E)10,578Course 124Form 00B24.Let f be a function such that f (x + h) f (x) = 6xh + 3h2 and f (1) = 5 .Determine f (2) - f (2) .(A)0(B)2(C)3(D)5(E)6November 200025Course 125.A manufacturers annual losses follow a distribution with density function2.53.52.5(0.6)for 0.6( ) 0otherwise.xf xx= To cover its losses, the manufacturer purchases an insurance policy with an annualdeductible of 2 .What is the mean of the manufacturers annual losses not paid by the insurance policy?(A)0.84(B)0.88(C)0.93(D)0.95(E)1.00Course 126Form 00B26.The price of gasoline changes over time. Over a period of three years, the rate of changein price increases for the first year, remains constant for the second year, and declines forthe third year. The rate of change in price is never negative over this time.Which of the following graphs best represents price graphed against time?(A)123PriceTime(B)(C)(D)(