STAT 479 Test 2 Spring 2013

Transcription

1 STAT 479 Test 2 Spring 2013 March 26, You have a sample 10 claims from a Pareto distribution. You are given that 10 X i 1 16,000,000. and 10 2 Xi i 1 i 12,000 Yi uses this information to determine the unbiased estimate of What was her estimate? 2.

2 2. He Insurance Company sells Hospital Indemnity policies. For each insured, the number of claims in a year are distributed as a Geometric distribution with a mean of 0.5. For each claim, the amount of the claim is distributed as a Gamma distribution with 3 and He Insurance Company has 2500 hospital indemnity policies. Assuming a normal distribution, calculate the probability that total aggregate claims in a year will be less 4,400,000.

3 3. Purdue Life Insurance Company is completing a lapse study on a 3 year term insurance policy. The following data is available: Life Date of Entry Date of Exit Reason for Exit Lapse Death Lapse Death Lapse Lapse Lapse Death Death Lapse Death Expiry of Policy Expiry of Policy Expiry of Policy Expiry of Policy Lapse Death Expiry of Policy Expiry of Policy Death Estimate S ˆ 20 (0.3) using the Nelson-Åalen estimator where lapse is the decrement of interest.

4 4. Chen Indemnity Incorporated provides warranty insurance on ipads. During each year, the number of expected claims per ipad is distributed as a Poisson distribution with a mean of The amount of each claim is distributed as follows: Amount of Claim Probability Chen Indemnity is providing warranty coverage on 50 ipads. Chen Indemnity purchases stop loss coverage from Scully Stop Loss Company. The stop loss coverage will cover aggregate claims in excess of the expected aggregate claims. Calculate the net stop loss premium.

5 5. You are given a sample from a uniform distribution from 0 to. You estimate using: ˆ 1.10 (,..., ) Max X1 X2, X n Calculate the bias in this estimator in terms of if n 20.

6 6. Claims are distributed as a Pareto distribution with 5 and You create a discrete distribution of the claims using the Method of Moment Matching with a span of 200 such that the mean of the discrete distribution is equal to the mean of the continuous distribution. Calculate the probability that claims will be less than 300 under the discrete distribution.

7 7. Purdue University provides life insurance on each employee. The amount of the life insurance is equal to the employee s salary. There are 2000 professors whose probability of death is Each professor s salary is uniformly distributed between 100,000 and 400,000. There are 500 support personnel whose probability of death is Each support personnel s salary is distributed as a Single Parameter Pareto with 6 and 20,000. Purdue purchases this life insurance from Lin Life Insurance Company. The premium is the expected aggregate claims plus the standard deviation of aggregate claims. Calculate the premium charged by Lin.

8 8. Gao Glass Company makes custom shaped light bulbs. Zheng, the company actuary, is studying the life expectancy of these light bulbs. Zheng records the following data for 140 light bulbs: Number of Months Until Number of Bulbs Failing Failure Zheng uses the Nelson-Åalen estimator to estimate H ˆ (5). Calculate the variance of this estimator.

9 9. Xinyao completes a six month study on the failure of iphones. There are 30 iphones in the study when the study starts. An additional 10 iphones enter the study at the end of 1 month and 30 additional iphones enter the study at the end of month 3. The following table lists the number of iphones that fail and the number that leave the study for other reasons (lost, replaced by a new phone, etc). Time Leaving Study Number of Failures Number of Other Terminations Use the Kaplan-Meier product limit estimator and the Greenwood approximation to determine the 80% linear confidence interval for S ˆ 70 (3) where failure is the decrement of study.

10 10. You are given the following table of medical claims for students in STAT 479: Claim Amount Number of Claims ,000 1 Using the Ogive, calculate the probability that the claim amount is between 800 and 2500.