Poisson Distribution Calculator

Calculate probabilities of the Poisson distribution step by step

The calculator will find the simple and cumulative probabilities, as well as the mean, variance, and standard deviation of the Poisson distribution.

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Your Input

Calculate the various values for the Poisson distribution with $$$\lambda = 11$$$ and $$$x = 10$$$.


Mean: $$$\mu = \lambda = 11$$$A.

Variance: $$$\sigma^{2} = \lambda = 11$$$A.

Standard deviation: $$$\sigma = \sqrt{\lambda} = \sqrt{11}\approx 3.3166247903554$$$A.

$$$P{\left(X = 10 \right)}\approx 0.119378060228025$$$A

$$$P{\left(X \lt 10 \right)}\approx 0.340510642465661$$$A

$$$P{\left(X \leq 10 \right)}\approx 0.459888702693687$$$A

$$$P{\left(X \gt 10 \right)}\approx 0.540111297306313$$$A

$$$P{\left(X \geq 10 \right)}\approx 0.659489357534339$$$A