Practice Questions 1

Practice Questions 1 - Practice Questions 1 ACTSC 431/831,...

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Practice Questions 1 – ACTSC 431/831, FALL 2011 1. Let Y be the total loss in an insurance portfolio and N be the number of claims in the portfolio. If N = 0, then Y = 0. If 1 N 5, then Y has an exponential distribution with mean 100. If N > 5, then Y has an exponential distribution with mean 200. It is given that Pr { N = 0 } = 0 . 3 , Pr { 1 N 5 } = 0 . 5 , and Pr { N > 5 } = 0 . 2 . (a) Let F Y ( y ) be the distribution function of Y . Calculate F Y ( y ) for all y ( -∞ , ). (b) Calculate the probability that the total loss in the portfolio will be greater than 500. (c) Calculate the probability of Pr { 0 < Y < 300 } . (d) Calculate the mean of the total loss. (e) Calculate the 20th percentile of the total loss. (f) Calculate the 80th percentile of the total loss. 2. The ground-up loss X for an insurance policy has a uniform distribution U (0 , 200). If X 80, the policy pays nothing; if 80 < X 120, the policy pays the amount of the loss above 80; if 120
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This note was uploaded on 02/08/2012 for the course ACTSC 431 taught by Professor Laundriualt during the Fall '09 term at Waterloo.

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Practice Questions 1 - Practice Questions 1 ACTSC 431/831,...

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