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Question:

Suppose there are number of accidents at location $A$ and location $B$ each day with Poisson Distribution with rate $0.001$ and the number of patients during each accident is Poisson distributed with rate $0.1$. Find the probability that the number of patients less than $3$ in one day.

Attempt:

So I did $E(N)=0.001\times 0.1=0.0001$ and then using this mean to find $$ P(X<3)=\sum_{0}^{2}Poi(0.0001) $$

and I got a value of $1$. I am sure this is the wrong answer. I need some help. Thank you!

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  • $\begingroup$ See my answer to your other question. Use PGFs. $\endgroup$
    – user218543
    Feb 25 '15 at 17:57
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This is an example of the Compound Poisson Distribution, you will need to use probability generating functions for the case where both the number of accidents and causalities are Poisson.

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