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hw1 - UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Actuarial...

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UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Actuarial Science Program DEPARTMENT OF MATHEMATICS Math 478 / 568 Prof. Rick Gorvett Actuarial Modeling Spring 2011 Homework Assignment # 1 (max. points = 10) Due at the beginning of class on Thursday, January 27, 2011 You are encouraged to work on these problems in groups of no more than 3 or 4. However, each student must hand in her/his own answer sheet. Please show your work – enough to show that you understand how to do the problem – and circle your final answer. Full credit can only be given if the answer and approach are appropriate. Please provide answers to two decimal places. Each problem is worth one point. (1) A loss distribution X has pdf 10 0 , 02 . 0 20 . 0 ) ( = x x x f . Find the value of the survival function at x = 7. (2) For the pdf in problem (1) above, find the hazard rate at x = 8. (3) Find the mean of a random variable X which has survival function x e , x 0. x S 0125 . 0 ) ( = (4) Find the ratio of the 90 th percentile to the median of the following distribution: x e x f 04 . 0 04 . 0 ) ( = , x
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