The Poisson Distribution
Explore
Find Probabilities
Formulas and Properties
The Poisson distribution specifies the probability of a certain number of events happening when each event occurs with a constant rate of λ.
Change the value of λ to see how the shape of the distribution changes. Hover over the bars in the graph to find the corresponding probability, or look at the table below.
Rate Parameter λ:
Probability Table:
Rate Parameter λ:
Type of Probability:
Value of x:
Value of x
1
:
Value of x
2
:
Show Probability Table
Probability Table:
The formula for the distribution function $P(X = x)$ of the Poisson distribution is shown to the right.
The distribution function $P(X=x)$ finds the probability of observing a count of $x$ events, when events occur with rate $\lambda$.
Rate Parameter λ:
Number of Events (x):
For calculations with values of λ or x not selectable via the sliders, please go to the
Find Probability
tab, where you can enter any values for λ and x.
Probability Table: