## Poisson Approximation to Binomial Distribution

Let $X$ be a binomially distributed random variable with number of trials $n$ and probability of success $p$.

The general rule of thumb to use Poisson approximation to binomial distribution is that the sample size $n$ is sufficiently large and $p$ is sufficiently small such that $\lambda=np$ (finite).

For sufficiently large $n$ and small $p$, $X\sim P(\lambda)$.

Poisson Approx. to Binomial Distribution
No. of Trials ($n$)
Probability of Success ($p$)
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Results
Mean ($\lambda$)
Standard deviation ($\sqrt{\lambda}$)
Required Probability :