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Unformatted text preview: 7e” w Eta/cc l. Amstutz Ant Farm is studying the life expectancy of ants. The farm’s actuary isolates 100
ants and records the following data: Estimate §(4) using the NelsonAalen estimator. 2. You are given the following frequency distribution: Number of Claims Probabili You are also given the following severity distribution: Amount of Claim Probabili Calculate Fs(350). 3. You are given the following frequency distribution: [:1
z .—
2 0.40
3 0.15 You are also given the following severity distribution: Calculate the Net Stop Loss premium for an aggregate deductible of 1000. 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 or = 3. Calculate the 90% conﬁdence interval for the expected aggregate claims if aggregate claims
are assumed to follow a normal distribution. 5. 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: Number of Probability of Claim
Students If a person is hospitalized, claims are distributed as a Gamma distribution with or = 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 uniformly from zero to 0. A sample of four
disability claims are drawn and used to estimate 0 by taking the maximum of the sample as
the estimate of 0. The true distribution of disability claims is a uniform distribution from zero to 1000. Calculate the Mean Square Error of our estimator. 7. 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. Calculate the probability assigned to the range that includes 100 under each method. 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 ofo = 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. 9. Troup Trucking Company suffered 100 accidents last year. The following table summarizes the amount of losses on those 100 accidents: 25,000 to 100,000
100,000 to 250,000
' Calculate F100(X) for losses between 25,000 and 100,000 using the Ogive. 10. Troup Trucking’s main competitor, Huang Hauling LTD, has the following accident information from last year: Amount of Loss Number of Accidents __
, 100,000 to 250,000 460 000
Over 250,000 740,000 Huang Hauling buys truck insurance which Will pay claims up to a limit of 100,000 per
claim. Using the distribution of claims from last year, calculate the expected value per payment for
the insurance company. ...
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 Spring '10
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