EX5 - AMS 410 Actuarial Mathematics Fall 2009 Exercise 5...

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Unformatted text preview: AMS 410 Actuarial Mathematics Fall 2009 Exercise 5: Discrete + Continuous 10/13/2009 1. Let X be a Poisson random variable with mean λ. If P [X = 1|X ≤ 1] = 0.08, what is the value of λ? 2. A probability distribution of the claim sizes for an auto insurance policy is given in the table below: Claim size 20 30 40 50 60 70 80 Probability 0.15 0.10 0.05 0.20 0.10 0.10 0.30 what is the standard deviation of claim sizes equal or greater than 40? 1 3. A company buys a policy to insure its revenue in the event of major snowstorms that shut down business. The policy pays nothing for the rst such snowstorm of the year and 10,000 for each one thereafter, until the end of the year. The number of major snowstorms per year that shut down business is assumed to have a Poisson distribution with mean 1.5. What is the expected amount paid to the company under this policy during a one-year period? 4. An insurance policy reimburses a loss up to a benet limit of 10. The policyholder's loss, Y , follows a distribution with density function f (y ) = 2 y3 0 for y > 1, otherwise. What is the expected value of the benet paid under the insurance policy? 5. The lifetime of a machine part has a continuous distribution on the interval (0, 40) with probability density function f , where f (x) is proportional to (10 + x)=2 . Calculate the probability that the lifetime of the machine part is less than 6. 2 ...
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