For a Binomial distribution to be approximated to Poisson (law of large numbers).

n should be big and p should be small.

In the proof I can see why n must be big,

but can some explain to me why must the probability be small?

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- Nov 29th 2010, 05:19 AMacc100jtPoisson approximation
For a Binomial distribution to be approximated to Poisson (law of large numbers).

n should be big and p should be small.

In the proof I can see why n must be big,

but can some explain to me why must the probability be small? - Nov 29th 2010, 02:23 PMmatheagle
so that np converges to lambda

the mean of both distributions are np and lambda, respectively

if p didn't go to zero inversely to n, then the mean would explode and you couldn't converge

to a distribution with a finite mean like a Poisson