Interarrival Times of a Poisson Process

• Pick an arbitrary starting point in time (call it 0).

• Let = the time until the next arrival.

  

• So

  

• has an exponential distribution!

Let = the time between the first and second arrival

• We can show that

  

  independently of !

• Similarly define as the time between the second and third arrival; as the time between the third and fourth arrival; . . .

• The random variables are called the interarrival times of the Poisson process.

The interarrival times, , are independent of each other and each have an exponential distribution with mean .