Exam3_v1 - AMS 410 Actuarial Mathematics Fall 2009 Exam 3:...

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Unformatted text preview: AMS 410 Actuarial Mathematics Fall 2009 Exam 3: Joint distributions, Version 1 11/19/2009, 6:50-8:00 pm 1. Let X and Y be discrete random variables with joint probability function f ( x,y ) = ( 2 x +1- y 9 for x = 1 , 2 and y = 1 , 2 , otherwise. Calculate E ( X Y ) . (A) 8 18 (B) 9 18 (C) 16 18 (D) 25 18 (E) 36 18 2. The distribution of Smith's future lifetime is X , an exponential random variable with a mean of 60 years, and the distribution of Brown's future lifetime is Y , an exponential random variable with a mean of 50 years. Smith and Brown have future lifetimes that are independent of one another. Find the probability that Smith outlives Brown. (A) 1 11 (B) 1 6 (C) 1 5 (D) 5 11 (E) 6 11 3. The future lifetimes (in months) of two components of a machine have the following joint density function: f ( x,y ) = ( 6 125 , 000 (50- x- y ) for < x < 50- y < 50 , otherwise. What is the probability that both components are still functioning 20 months from now?...
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Exam3_v1 - AMS 410 Actuarial Mathematics Fall 2009 Exam 3:...

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