MathLivePoisson distribution probability mass function
Gives the probability that a discrete random variable with rate parameter lambda takes the value x, for counts of events occurring independently at a constant average rate. It is used for modelling the number of events in a fixed interval of time or space.
P(X = x) = \frac{\lambda^x e^{-\lambda}}{x!}What the symbols mean
| probability that the random variable X equals x | |
| discrete random variable counting the number of events | |
| non-negative integer number of events observed | |
| average number of events in the interval (rate parameter, dimensionless) | |
| Euler's number, base of the natural logarithm | |
| factorial of x |
About this formula
- FieldStatistics
- TopicProbability distributions
- LevelUniversity
- Also calledPoisson probability mass function, Poisson distribution formula, probability of k events Poisson, law of small numbers, Poisson pmf, probability of x events in fixed interval
- SourceWikidata Q205692
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