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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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
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