# Poisson Distribution Calculator

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

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

## Your Input

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

## Answer

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