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S479 F09 Test 2 Solutions

# S479 F09 Test 2 Solutions - 1 Amstutz Ant Farm is studying...

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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 Nelson-Aalen 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 poi-Elk 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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S479 F09 Test 2 Solutions - 1 Amstutz Ant Farm is studying...

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