Waiting Time for Poisson Process obeys Exponential Distribution/Examples/Arbitrary Example 1

Example of Use of Waiting Time for Poisson Process obeys Exponential Distribution

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.

Proof

From Waiting Time for Poisson Process obeys Exponential Distribution, the waiting time of $P$ is $\dfrac 1 4$.

Hence the result.

$\blacksquare$

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): exponential distribution
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): exponential distribution