Question

Suppose the arrival rate is 5. What is the mean interarrival time? Express your answer rounded to 3 decimal places. For example, 10.123.

Answer 1

Arrival rate is 5 hence 5 arrivals per time unit,

So assuming the arrival to follow poisson process we get that that inter arrival time follows an exponential distribution with parameter 5. Need to find the mean of interarrival time

Let T be the inter arrival time then T ~ exp(5), so

So   

Above is a standard result i.e., mean of exponential(a) is equal to 1/a.

So Mean Arrival time is 1/5 time units