This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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'¥:[email protected]~—> 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 [email protected]
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) ...
View
Full Document
 Spring '10
 NA

Click to edit the document details