Free Poisson Probability Calculator
Calculate the probability of observing exactly k events in a fixed interval when events occur at a known average rate lambda.
P(X = k)
0.14652511
Expected Value4.0000
Standard Deviation2.0000
P(X = k) vs Average Rate (lambda)
How to Calculate Poisson Probability
Formula
P(X = k) = (lambda^k * e^(-lambda)) / k!
The Poisson distribution models the number of events occurring in a fixed interval of time or space, when events happen independently at a constant average rate lambda. Both the mean and variance equal lambda.
Example Calculation
A call center receives an average of 4 calls per hour. What is the probability of exactly 2 calls in an hour?
- 01lambda = 4, k = 2
- 02P(X=2) = (4^2 * e^(-4)) / 2!
- 03= (16 * 0.01832) / 2
- 04= 0.29305 / 2
- 05= 0.14653
Frequently Asked Questions
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