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1. ## Poisson Mixture problem

Nov 2000 #13
A claim count distribution can be expressed as a mixed Poisson distribution. The mean of the Poisson distribution is uniformly distributed over the interval [0,5].
Calculate the probability that there are 2 or more claims.

I know the way i solved this question is wrong. Can you help me identify why my logic is flawed

I let X represent the mixed poisson distribution

E(X) = E(E(X|lamba )) = E(lamba) = mean of uniform [0, 5] = 2.5

P(X>= 2) = 1- P(x =0) - P(x =1) = 1- e(-2.5) -2.5e(-2.5) = 0.71

The answer 0.61 and is solved by this method (number 137) http://math.illinoisstate.edu/actuary/examm/m-09-05.pdf

2. Originally Posted by liltich
Nov 2000 #13
A claim count distribution can be expressed as a mixed Poisson distribution. The mean of the Poisson distribution is uniformly distributed over the interval [0,5].
Calculate the probability that there are 2 or more claims.

I know the way i solved this question is wrong. Can you help me identify why my logic is flawed

I let X represent the mixed poisson distribution

E(X) = E(E(X|lamba )) = E(lamba) = mean of uniform [0, 5] = 2.5

P(X>= 2) = 1- P(x =0) - P(x =1) = 1- e(-2.5) -2.5e(-2.5) = 0.71

The answer 0.61 and is solved by this method (number 137) http://math.illinoisstate.edu/actuary/examm/m-09-05.pdf
You cannot simply find the mean of lambda by (5/2).

P(0)= 1/5 * integral from 0 to 5 (e^(-lambda)) d(lambda)
This is the right way. you should be able to read it even it is messy.