Waiting Time for Poisson Process obeys Exponential Distribution
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Theorem
Let $P$ be a Poisson process in which events occur at a rate of $k$ per unit time.
Then the waiting times of $P$ are exponentially distributed with expectation $\dfrac 1 k$.
Proof
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Examples
Arbitrary Example
Let $P$ be a Poisson process in which events occur at a rate of $4$ per hour.
Then the mean waiting time of $P$ is $15$ minutes.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): exponential distribution
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Poisson process
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): exponential distribution
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Poisson process