S479 F09 Test 1

# S479 F09 Test 1 - Stat 479 Test 1 October 6 2009 There are...

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Stat 479 Test 1 October 6, 2009 There are only eight questions on the test. However, the first question has 8 parts and is worth 30 points. The other seven questions are worth 10 points.

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1. You are given the following empirical distribution for the random variable X which is the claim amount for a policy covers doctors office visits: Claim Amount Probability of Claim 10 0.20 20 0.25 30 0.30 40 0.15 50 0.10 Calculate the following: (a) E[X] (b) Var(X) (c) e(20) (d) E[(X-20) + ] (e) E[(X Λ 40)] (f) VaR 0.80 (X) (g) TVaR 0.80 (X) (h) An insurance company has 2500 claims. Assume each claim is independent and that the aggregate claims follow a normal distribution. Determine the probability that the claims will exceed \$69,000.
Claims for a cancer policy are distributed as a two point mixture distribution. The claims are distributed as a Pareto distribution with α = 4 and θ with a weight of 0.2 and as a Gamma distribution with α = 4 and θ = 1000 with a weight of 0.8. The expected value of claims is 4000.

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S479 F09 Test 1 - Stat 479 Test 1 October 6 2009 There are...

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