STA3007_0506_t10

# STA3007_0506_t10 - STA 3007 Applied Probability Tutorial 10...

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STA 3007 Applied Probability 2005 Tutorial 10 A The Uniform Distribution and Poisson Processes (a) Theorem 3.6 Let W 1 ,W 2 ,... be the occurrence times in a Poisson process of rate λ > 0. Conditioned on X ( t ) = n , the random variables W 1 ,W 2 ,...,W n have the joint probability density function f W 1 ,...,W n | X ( t )= n ( w 1 ,...,w n ) = n ! t - n for 0 < w 1 < ··· < w n t. Example i. An insurance company pays out claims on its life insurance policies in accordance with a Poisson process having rate λ = 5 per year. If the amount of money paid on each policy is \$2000, what is the expected present value of the total payment in a four-year span when the discount rate is β ? 1

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B Compound Poisson Processes Given a Poisson process X ( t ) of rate λ > 0, suppose that each event has associated with it a random variable, possibly representing a value or a cost. Examples will appear shortly. The succes- sive values Y 1 ,Y 2 ,... are assumed to be independent, independent of Poisson process, and random
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## This note was uploaded on 05/21/2011 for the course STA 3007 taught by Professor Kb during the Spring '11 term at CUHK.

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STA3007_0506_t10 - STA 3007 Applied Probability Tutorial 10...

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