Homework_Assignment_14 - 3 ] = 314 Determine the expected...

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Homework Assignment 14: (1) Do Exercise 12.13 on page 394. (2) Lucky Lisa finds coins on her way to class at a Poisson rate of 0.5 coins per minute. The denominations are randomly distributed: (i) 60% of the coins are pennies; (ii) 20% of the coins are nickels; (iii) 20% of the coins are dimes. Calculate the conditional expected value of the coins Lisa found during her one-hour walk today, given that among the coins she found there were exactly ten nickels. (Ans $1.28) (3) S has a compound Poisson distribution with: (i) individual claim amounts equal to 1, 2 or 3; (ii) E(S) = 56; (iii) Var(S) = 126; and (iv) E[ (S-E[S])
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Unformatted text preview: 3 ] = 314 Determine the expected number of claims of size 2. (Ans 11) A compound Poisson distribution can be represented by the following sum: S= (1) N 1 + (2) N 2 + (3) N 3 . Suppose that = 20, p(1) = .7, p(2) = .2, and p(3) = .1. Compute f S (x) for x = 0, 1, 2, 3 by calculating the convolution of the distributions of (1) N 1 , (2) N 2 , and (3) N 3 , as in the Alternative Method Calculations on page 382. (Ans f S (0) = e-20 , f S (1) = 14e-20 , f S (2) = 102e-20 , and f S (3) = 515.33e-20 ) (5) Use the recursive method to verify your computations in problem (4)....
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This note was uploaded on 05/11/2011 for the course STOR 472 taught by Professor Charlesdann during the Spring '11 term at University of North Carolina School of the Arts.

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