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Unformatted text preview: AMS 410 Actuarial Mathematics Fall 2009 Exam 2: Univariate distributions, Version 1 10/27/2009, 6:50-8:00 pm 1. Let X be a random variable with moment generating function M X ( t ) = ( 2 + e t 3 ) 9 ,- < t < Calculate the variance of X . (A) 11 (B) 9 (C)8 (D) 3 (E)2 2. An insurance policy on an electrical device pays a bene t of 4000 if the device fails during the rst year. The amount of the bene t decreases by 1000 each successive year until it reaches 0. If the device has not failed by the beginning of any given year, the probability of failure during that year is 0.4. What is the expected bene t under this policy? (A) 2234 (B)2400 (C) 2500 (D) 2667 (E) 2694 3. Let X be a continuous random variable with density function f ( x ) = ( | x | 10 for- 2 x 4 otherwise . Calculate the expected value of X . (A) 12 5 (B) 28 15 (C) 1 (D) 3 5 (E) 1 5 4. In a small metropolitan area, annual losses due to storm, re, and theft are assumed to be independent, exponentially distributed random variables with respective means 1.0, 1.5, andindependent, exponentially distributed random variables with respective means 1....
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This note was uploaded on 08/08/2010 for the course AMS 410 taught by Professor Yang,y during the Fall '08 term at SUNY Stony Brook.
- Fall '08