# Comparison of Binomial and Poisson models w.r.t. range of values one can obtain from each model

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Q: An actuarial student has said "the binomial model is better than the Poisson model because values of a binomial distribution are limited to the range 0,1,2,....N, whereas the Poisson RV can take on any of the values 0,1,2,... But clearly, the number of deaths cannot be greater than the total population." Comment on the student's statement.

I think the student is correct with saying that the number of deaths cannot be greater than the total population.

I have also read that probabilities of values greater than N under the Poisson Model are negligible. Does this mean we ignore the fact that the Poisson give more values? If so, how do we then compare the two models with respect to the range of values of death? (keeping in mind that the question is 4 marks)

$N$ will typically be a very large number, which in turn makes $E_x^C$ very large. Now, since your Poisson probability mass function for the Poisson model contains an exponential term, values greater than $N$ will be VERY small.