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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
1323 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 NelsonAalen 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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