Poisson Distribution Calculator

The calculator will find the Poisson 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 $$$x = 10$$$.

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

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

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

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

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