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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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 Fall '08
 Yang,Y
 Variance, Probability theory

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