S479 F10 Test 2 Solutions

S479 F10 Test 2 Solutions - STAT 479 Test 2 November 9,...

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Unformatted text preview: STAT 479 Test 2 November 9, 2010 1. You are given the following grouped claim information: Amount of Claim Number of Claims Total Amount of Claims J 0 - 5000 8 24,000 5000 - 10,000 12 96,000 | 10,000 — 25,000 l 3 55,000 25,000 — 100,000 2 l 150,000 1 | 125,000 26 l 100,000 + Total 450,000 Calculate E(XA10,000) and E(XA40, 000). Q, L; 1:900 v55 1%???) Emw&w;rwfla\€fll‘fzfl2¥flfiw'W/X'Jlnwg M Sim WMMQW 53*- H 1:492:11 , J «:2 mi A?” ‘91 W 2. The number of dental insurance claims follow a Poisson distribution with an expected number of claims of 2. The amount of each dental claim has the following distribution: l Amount of Claim Probability of Claim I 100 0.50 l 200 0.25 | l 300 | 0.20 | 400 l 0.05 Dunham Dental Insurance Company has 2000 independent insureds with dental insurance. Use the normal approximation to estimate the probability that aggregate claims will exceed 700,000 in a given year. if (>53 :5 (l fl. 2?} 3. The number of dental insurance claims follow a Poisson distribution with an expected number of claims of 2. The amount of each dental claim has the following distribution: Amount of Claim | Probability of Claim 100 l 050 200 | 025 300 | 020 400 | 005 Calculate fs(400) for a person with dental insurance. @éDQ 4;?“ / mm i < C? mfl é? {:23 £113 :2 {1 i 9m «:1 ’ iflfigrfiéy r F g ,2 fig» wig» if; °3’ (“gxfi % Tfig 4. Warranty claims for laptop computers follow a Pareto distribution with a = 5 and (9 = 2000. Chengyin decides to discretize this distribution using a span of 200. fR (600) is the probability assigned to the value of 500 using the Method of Rounding. fMM (600) is the probability assigned to the value of 500 using the Method of Moment Matching. Calculate 1000{ fR (600)— fMM (600)} . 5. The following information on students in the actuarial program at Purdue is used to complete an analysis of students leaving the program because they are switching majors. Student | Time of Entry Time of Exit Reason for Exit 1 O .5 Switching Major _ l 0 Switching Major ‘ W O 2 L Switching Major 0 3 Graduation 8 O 3, Switching Major 9—12 0 3.5 Graduation 13-23 0 Graduation 24, 0.5 2 Switching Major 25 0.5 3 Switching Major 26 1 3.5 Graduation 27 l 1 4 Switching Major 28 l 1.5 4 Graduation 29/ | ’2 5 Graduation 30 l 3 5 Graduation 1:1(3) is estimated using the Nelson-Aalen estimator. Calculate the 90% linear confidence interval for 19(3). \l >< 5 r“ rim .1 .5 l 2 l Ll Mr 3 2» 2.... 35 Ll 6. The following information on students in the actuarial program at Purdue is used to complete an analysis of students leaving the program because they are switching majors. Student | Time of Entry Time of Exit Reason for Exit 1 I O .5 Switching Major 2—5 l o 1 Switching Major 6 l O 2 Switching Major 0 3 Graduation V O 3 Switching Major 0 3.5 Graduation 0 Graduation 0.5 2 Switching Major 0.5 3 Switching Major I 1 3.5 I Graduation | 1 4 | Switching Major | 1.5 4 | Graduation | 29 | 2 5 | Graduation l 30 | 3 5 | Graduation 5(x) is estimated using the product limit estimator. Estimate Var[S3O (2)] using the Greenwood approximation. \lcl $309)] if, is (QT 3}; Ll / yam MVWW wk? W “53” (MW 932“ 3 (jaaDWD Wt g 7. Ab Ghani Automobile Insurance Company received the following claims under an automobile insurance policy: 100 100 200 200 250 300 300 300 400 700 Calculate EOQOO) using the Empirical Distribution Function. r: “immimv W Calculate fi(200) if the distribution is smoothed using the uniform kernel with a bandwidth of 100. \ :i / m3 3f /0 l $2 a Q "$90 {:13 l ' V L f if Q m r 5:2 HQ 8. Ab Ghani Automobile insurance Company received the following claims under an automobile insurance policy: 100 100 200 200 250 300 300 300 400 700 ZX=2850 and ZXZ=1,082,500 The company’s Chief Actuary, Rahim, creates a continuous distribution using a Kernel Density model with a triangular kernel with a bandwith of 100. Rahim then uses this Kernel Density model to calculate the premium to be charged. The premium is calculated as the mean plus one standard deviation. alculate the premium. m K tiriw m MW” ya... M“: W ~23» c ;8 Mill. (at; 9. You are given: i. The frequency distribution for claims is distributed as a geometric distribution with ,6 = 2. ii. The severity distribution for claims is distributed as follows: | Amount of Claim l probability l l 400 l 0.5 l | 800 l 0.4 l | 1000 l 0.1 l Sutton Stop Loss LTD provides stop loss coverage with an aggregate deductible of 1000. Calculate the net stop loss premium. € W 33—3. / 10. You are given the following sample: X: 10 20 3O 40 50 The following estimator is used to estimate 0'2 : Eon—X? n+1 Calculate the bias in this estimator. (A h b la; a?! a?“ 9W" ...
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S479 F10 Test 2 Solutions - STAT 479 Test 2 November 9,...

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