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