Poisson Distribution Calculator

Instructions: Compute Poisson distribution probabilities using the form below. Please type the population mean (λ), and provide details about the event you want to compute the probability for:

Population mean (\(\lambda\))
≤ X ≤
X ≤
X ≥

Poisson Probability Calculator

More about the Poisson distribution probability so you can better use the Poisson calculator above: The Poisson probability is a type of discrete probability distribution that can take random values on the range \([0, +\infty)\). The main properties of the Poisson distribution are:

  • It is discrete, and it can take values from 0 to \(+\infty\).

  • The type of skewness depends on the population mean (\(\lambda\))

  • It is determined by the population mean (\(\lambda\))

  • Its mean is \(\lambda\) and its population variance is also \(\lambda\)

Using the above Poisson distribution curve calculator , you are able to compute probabilities of the form \(\Pr(a \le X \le b)\), of the form \(\Pr(X \le b)\) or of the form \(\Pr(X \ge a)\). Type the appropriate parameter for \(\lambda\) in the text box above, select the type of tails, specify your event and compute your Poisson probability.

The Poisson probability formula is

\[ \Pr(X = k) = \displaystyle \frac{e^{-\lambda} \lambda^k}{k!}\]

This Poisson distribution calculator with steps corresponds to a solver for a discrete distribution. We have other discrete distribution calculators that you may be interested in, such as our Binomial distribution calculator , Geometric distribution calculator , and Hypergeometric distribution calculator , to mention a few of them.

Also, you can use our general discrete probability calculator which will provide you with the mean and standard deviation of a generic discrete distribution.

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