Poisson Probability

Probabilities for counts of events in an interval, with poissonpdf and poissoncdf.

Inputs

Probability that X is

Results update as you type.

Results

P(X = 2) = 0.1850

The probability of exactly 2 events in the interval is 0.1850, or about 18.50%.

Poisson (μ = 3.5) probability bars for x = 0 to 12. The highlighted bars are the outcomes exactly 2; together they have probability 0.1850.0123456789101112x

Results

P(X = 2)0.1850
Mean μ3.5
Standard deviation σ1.8708

On the TI-84

2nd VARS (DISTR) → C:poissonpdf( for “exactly”, or D:poissoncdf( for “at most”.

poissonpdf(3.5, 2)

Show steps
  1. Formula. P(X = x) = μx e−μ ÷ x! = 3.52 e−3.5 ÷ 2! = 0.1850
  2. Mean and SD. μ = 3.5, σ = √μ = 1.8708.

About this calculator

When to use Poisson

The Poisson distribution models the number of times an event happens in a fixed interval of time or space, such as calls per hour or typos per page, when events happen independently at a steady average rate μ (sometimes written λ).

For a Poisson distribution the mean and the variance are both μ, so the standard deviation is √μ. There's no upper limit on X, so "at least" problems use the complement.