# 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.

### 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**