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Unformatted text preview: 1. Amstutz Ant Farm is studying the life expectancy of ants. The farm’s actuary isolates 100
ants and records the following data: Number of Days till Death Number of Ants Dying 7 (J
1 6 my C?
2 10 63W“
3 12 3 Li
4 20 “I 9W
5 35
6 10
7 3
8 2
9 1
10 1 Estimate §(4) using the NelsonAalen estimator. 2. You are given the following frequency distribution:  Number of Claims I Probability I
I 0 I 0.20 I
1 I 0.25 I
2 I 0.40 I
3 I 0.15 I You are also given the following severity distribution: Amount of Claim Probability
100 0.50
I 200 0.40
I 500 0.10 Calculate FS(3 5 0). F6 (550): 3200 I» «I3 I £00; a “ﬁg/30:3) 9;: {MD} a V
.22 z: (;Z§y%®4w<9>(¢5>a a at? 3, i? [WWI {722.436 if 13:” (01‘5’2) o PF'ng/QQ if?! (“I a) f
V :3 J H, (I):a(;§j§ $1 .1761?“ £0 (.vI(’vf>i>Z'¥:I@~—> at 1C? Ia Oi lag foam» 000020 35390) “Z O 3. You are given the following frequency distribution: Number of Claims } Probability l
0 p 0.20 l
1 l 0.25 I
2 l 0.40 l
3 l 0.15 You are also given the following severity distribution: Amount of Claim Probability
100 0.50
200 0.40
500 0.10 Calculate the Net Stop Loss premium for an aggregate deductible of 1000. 5}; JV ;:
LAB 9‘ QM Wyﬁ ‘Q/XC lé’zfﬂf W ‘4’ wig, AW \ 65.1 5134) ‘ raw
3 (jams win, 13/“ £
(31 (j V 9 a) ’00 SLEDGE
J’ﬂma WNW“ ” 4. The number of claims under a ﬁve year medical insurance policy is distributed as a Poisson
distribution with a mean of 100. The severity of claims is distributed as a Pareto
distribution with 0 = 1000 and at = 3. Calculate the 90% conﬁdence interval for the expected aggregate claims if aggregate claims
are assumed to follow a normal distribution. Vow 00:” /@C> E m); Mo . Sahlin Health Insurance Company is providing all students in STAT 479 With a health insurance policy. The health insurance policy provides payment if a person in this class is
hospitalized with HlNl. The following table is a census of the students covered and their probability of claim: Gender Number of Probability of Claim
Students
Female l 12 0.05
Male l 16 0.10 If a person is hospitalized, claims are distributed as a Gamma distribution with OL = 2
and 0 = 2000 Without regard to gender. Claims are independent. Calculate E(S) and Var(S). 6. Disability claims are assumed to be distributed unifome from zero to 6. A sample 0@
disability claims are drawn and used to estimate 9 by taking the maximum of the sample as
the estimate of 9. The true distribution of disability claims is a uniform distribution from zero t ‘1 Calculate the Mean Square Error of our estimator. [wager r», A ll @357 war/5 b” Vail/51>»? . Dental claims are distributed exponentially with 9 = 100. You want to discretize the claims
using a span of 20 using both the Method of Rounding and the Method of Moment
Matching Where you will match the mean. I/ , ﬂaw:93W‘Mt’“”“”’“wm&w ‘ V Calculate the probability assigned toghggznge that includmnder each method. ta Qﬁiws poiElk in: 2Q own? 8. You are given the following sample data:
X: 5, 6, 8,10,10,10, 13,17, 20, 21
You are also given: N = 10
Sum oin = 120
Sum of X12 = 1724 You complete Hypothesis Testing with: H0: The mean is 10.
H1: The mean is not 10. Calculate the 2 statistic, the critical value(s) assuming a signiﬁcance level of 30%, and the
p value. State your conclusion with regard to the Hypothesis Testing. IO 5
/l ggxﬂvwﬂ ‘ \lauf 0‘) T: 9. Troup Trucking Company suffered 100 accidents last year. The following table
summarizes the amount of losses on those 100 accidents: Amount of Loss +_Number of Accidents ‘
0 to 10,000 15 I
10,000 to 25,000 25 \
25,000 to 100,000 35 1
100,000 to 250,000 20 
Over 250,000 5 I Calculate F100(X) for losses between 25,000 and 100,000 using the Ogive. )9 1e ﬂiean W Z mmr TMLWW 10. Troup Trucking’s main competitor, Huang Hauling LTD, has the following accident information from last year: Amount of Loss ‘ Number of Accidents l Total Loss i 0 to 10,000 4 5 1 30,000 10,000 to 25,000 \ 8 130,000 1
25,000 to 100,000 \ 12 840,000
100,000 to 250,000 \ 3 460,000
Over 250,000 \ 2 740,000 Huang Hauling buys truck insurance which will pay claims up to a limit of 100,000 per ,
claim. 1 Using the distribution of claims from last year, calculate the expected value per payment for
the insurance company. I “ 220:5 wart/11:01:11,919
SQJDCDC) 79w IEDIQQQ a), 5%QQQQW3d/M) ;. 45120;, 1:300? , Wumbw pg ﬂaﬁwmﬁ ~< w )S'ba 1900:"; C / $
in Mﬂcjﬁj L: ﬁg?” 60/ OZ) ...
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This note was uploaded on 03/15/2012 for the course STAT 479 taught by Professor Na during the Spring '10 term at Purdue UniversityWest Lafayette.
 Spring '10
 NA

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