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
मानक विचलन2.0000

P(X = k) vs Average Rate (lambda)

सूत्र देखें →

सूत्र

## 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.

हल किया गया उदाहरण

A call center receives an average of 4 calls per hour. What is the probability of exactly 2 calls in an hour?

  1. 01lambda = 4, k = 2
  2. 02P(X=2) = (4^2 * e^(-4)) / 2!
  3. 03= (16 * 0.01832) / 2
  4. 04= 0.29305 / 2
  5. 05= 0.14653