STAT 479 Spring 2024 Sample Exam 2

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Apr 3, 2024

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STAT 479 Sample Exam 2 Spring 2024 There are 9 questions on this exam. The point value of each question is shown by the question number. There are 100 points on this exam. When you are finished you may turn in your exam and leave. However, no one may leave the exam room during the final five minutes of the exam period. Failure to stop writing when time has expired may result in a grade of zero for your exam. If you believe that a question is defective, write your reason on your exam paper. Calculation type questions require supporting work to receive full credit. A question with a correct numerical answer and no supporting work will receive no credit. If you cheat on this exam your semester grade for this course will be an F. Some examples of cheating are: Allowing another student to see your paper during the exam period. Looking at another student’s paper during the exam period. Using notes during the exam period. Looking at your phone during the exam period. Altering your answer to a question after your paper is graded and asking that your paper be re-graded. Please be considerate of the students around you. If your exam paper is not signed it will not be graded. I have read the statements on this page. I understand the statements on this page. Your Name (PRINT): ______________________________________________ Your Signature: __________________________________________________

1. (5 points) A warranty insurance product has an upper limit of 5000. You are given the following sample information about claims paid: 1000 2000 3000 4000 5000 5000 5000 You want to model claims paid for this warranty product using an Exponential distribution. Calculate the Maximum Likelihood Estimator ϴ.

2. (10 points) You are analyzing data for dental claims from DDD Insurance company. During 2023, there were 100 policies in force. The number of claims under each policy was distributed below: Number of Claims Number of Policies 0 10 1 25 2 40 3 14 4 7 5 0 6 4 You believe that claims should be modeled as a Poisson Distribution. You want to develop am 80% confidence interval for λ using the Maximum Likelihood Estimator for λ Determine the confidence interval for λ. )

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3. The data below may look familiar. Quinto believes that the data should be modeled using a binomial distribution. a. (5 points) Determine the maximum likelihood estimate of q given that m = 9. Number of Claims Number of Policies 0 10 1 25 2 40 3 14 4 7 5 0 6 4 b. (5 points) If m is unknown, describe the process of determining the MLE estimates for q and m. (A complete answer will cover at least 5 unique steps.

4. The following grouped data is being analyzed: Amount of Claim Number of Claims 0 – 200 8 200-400 9 400 + 3 The claims are being modeled as an exponential distribution with ϴ derived from the Maximum Likelihood Estimator. a. (10 points) Determine ϴ. b. (5 points) If the claims are to be modeled Uniform (0,ϴ), determine the Maximum Likelihood estimator of ϴ.

5. (10 points) You are given the following data from an Exponential distribution: 20 22 26 32 40 42 49 60 You estimate the parameter ϴ of the exponential distribution using percentile matching with the 30 th percentile of the smoothed empirical distribution. Calculate 𝜃 ෠ .

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6. (10 points) You are given the flowing data from a Gamma distribution: 1500 2000 3200 4500 You estimate the parameters of the Gamma Distribution using the method of moment matching. State the estimated parameters.

7. Jack buys marine insurance coverage from Rose Insurance Company. Over the next 8 years, Jack has claims of: 0, 0, 400, 500, 1000, 1300, 2000, 2000 The number of claims is assumed to be distributed as a Poisson distribution. a. (7 points) Calculate the criterion for full credibility (the number of claims) for the total number of claims to be within 8% of the true total number of claims at least 70% of the time. b. (7 points) Calculate the criterion for full credibility (the number of claims) for the pure premium in this situation to be within 8% of the true value of the pure premium at least 70% of the time.

c. (6 points) Rose’s manual premium is 1000. Using partial credibility, determine the premium Rose should charge Jack in the next year.

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8. (10 points) Danielle buys an Inland Marine policy with a disappearing deductible from F & Sons Trucking Insurance. The policy pays zero if the loss is less than 100,000 and pays 100% of the loss if the loss is 900,000 or greater. Danielle has a loss and receives a payment of 560,000 from F & Sons. Determine the amount of the loss. 9. (10 points) Mitchell purchases a homeowner’s policy from N F Way Housing Insurance on his house in Florida. The policy has an 80% coinsurance provision. Mithcell’s house is insured for 400,000. The home was worth 410,000 on the day the policy was purchased. There is one hurricane – just one - that causes 250,000 worth of damage. On the date of the hurricane, the house was worth 550,000. Calculate the benefit payment that Mitchell will receive under his policy.

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