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# EX4 - AMS 410 Actuarial Mathematics Fall 2009 Exercise 4...

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Unformatted text preview: AMS 410 Actuarial Mathematics Fall 2009 Exercise 4: Discrete random variables 10/06/2009 1. An insurance policy pays an individual 100 per day for up to 3 days of hospitalization and 25 per day for each day of hospitalization thereafter. The number of days of hospitalization, X , is a discrete random variable with probability function: P (X = x) = 6−k 15 0 k = 1, 2, 3, 4, 5 otherwise Calculate the expected payment for hospitalization under this policy. 2. An actuary determines that the claim size for a certain class of accidents is a random variable, X , with moment generating function MX (t) = 1 (1 − 2500t)4 Determine the standard deviation of the claim size for this class of accidents. 3. A fair die is tossed and a number turns up. Given that it is greater than 2, what's its expected value? 1 4. An actuary has discovered that policyholders are three times as likely to le two claims as to le four claims. If the number of claims led has a Poisson distribution, what is the variance of the number of claims led? 5. As part of the underwriting process for insurance, each prospective policyholder is tested for high blood pressure. Let X represent the number of tests completed when the rst person with high blood pressure is found. The expected value of X is 12.5. Calculate the probability that the sixth person tested is the rst one with high blood pressure. 6. A small commuter plane has 30 seats. The probability that any particular passenger will not show up for a ight is 0.10, independent of other passengers. The airline sells 32 tickets for the ight. Calculate the probability that more passengers show up for the ight than there are seats available. 2 ...
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EX4 - AMS 410 Actuarial Mathematics Fall 2009 Exercise 4...

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