POISSON AND EXPONENTIAL
Analysis of the relationship between the two random variables
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A Poisson random variable is related to the exponential random variable. Here is the derivation:
- A Poisson random variable X is good for counting the number of events in a given interval. If that interval has a length T, then the Poisson random variable describes the number of events in an interval of length T.
- The mathematics of the derivation are the same as for the relationship between a geometric and an exponential random variable.
- The average number of events in an interval is a, the size of the interval, T and the average distance between two events is lambda. The parameters a, lambda and T are related by
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RELATED
CONCEPTSRandom Variables Probability Mass Function Cumulative Distribution Function Expectation of a Discrete Random Variable Important Discrete Random Variables ![]()
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