# 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.

## 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**