Poisson Distribution Simulator

Simulate event count probabilities from an average rate

Lambda average rate

Event count k

Poisson Formulas

Probability	P(X = k) = e^-lambda lambda^k / k!
Mean	lambda
Variance	lambda
Standard deviation	sqrt(lambda)

Step-by-Step Example

If lambda = 4 and k = 3, then P(X = 3) = e^-4 x 4^3 / 3!. This gives about 19.54%, meaning exactly 3 events is a plausible outcome when the average count is 4.

When to Use It

Counting arrivals, calls, defects, or events in a fixed interval.
Events occur independently.
The average rate is approximately constant.
Two events are unlikely to happen at exactly the same instant.

Frequently Asked Questions

What is a Poisson distribution?▼

A Poisson distribution models the number of events that occur in a fixed interval when events happen independently at an average rate.

What is lambda in a Poisson distribution?▼

Lambda is the expected average number of events in the interval.

What is the Poisson probability formula?▼

The formula is P(X = k) = e^-lambda lambda^k / k!.

What are the mean and variance?▼

For a Poisson distribution, both the mean and variance equal lambda.

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