# STAT 302 Chapter Notes - Chapter 5.2: Binomial Distribution, Poisson Distribution

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Poisson approximation to Binomial distribution

Okay, so we know that the limit for a Binomial distribution is fixed to the value of n.

Now, if the value of n is very high and the value of p is very low in a Binomial

distribution, which does not that as we go along increasing X, then the values of the

individual probabilities goes on decreasing, as we need to take into account the

increasing value of nCx with that of p*X, but if we look at np, that is the mean of the

binomial distribution, we would realize that when n reaches infinity and p reaches 0,

then np gets the constant value of λ, which can be used to approximate the binomial

distribution as Poisson distribution.

Here is the corresponding proof:

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