Poisson Distribution Calculator

Poisson distribution calculator is used to find the probability and cumulative probabilities for Poisson random variable given the mean number of successes ($\lambda$).

Poisson Distribution Calculator
Average rate of success ($\lambda$):
Number of success (x):
Result
Probability : P(X = x)
Cumulative Probability : P(X ≤ x)
Cumulative Probability : P(X < x)
Cumulative Probability : P(X ≥ x)
Cumulative Probability : P(X > x)

Poisson Distribution

A discrete random variable $X$ is said to have Poisson distribution with parameter $\lambda$ if its probability mass function is

$$ \begin{aligned} P(X=x)& =\frac{e^{-\lambda}\lambda^x}{x!},\ & \hbox{$x=0,1,2,\cdots$;$\lambda>0.$} \
\end{aligned} $$

where

  • $\lambda=$ mean number of successes.

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