Proof Binomial to Poisson Distribution

In this class, We discuss Proof Binomial to Poisson Distribution.

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The reader should have prior knowledge of poisson distribution. Click Here

We understand how we got the probability mass function of the Poisson distribution.

In poisson we have λ value.

λ = np

p = λ/n

Assumption: n -> ∞ and p -> 0

In the coming classes, we discuss why we assume n -> ∞ and p -> 0.

The below diagram shows the proof of Binomial to Poisson distribution.

We take the binomial distribution equation.

We derive the probability mass function of Poisson distribution with an assumption n -> ∞ and p -> 0.

Proof: Poisson probability mass function is a discrete probability function

In binomial distribution as n = 10

The random variable X is having values 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

In poisson n -> ∞

The random variable X = 0, 1, 2, . . , ∞

The below diagram shows the proof sum of all probabilities in Poisson = 1.