Solution Found!
An argument similar to that of Exercise 4.168 can be used
Chapter 4, Problem 169SE(choose chapter or problem)
Problem 169SE
An argument similar to that of Exercise 4.168 can be used to show that if events are occurring in time according to a Poisson distribution with mean λt, then the inter arrival times between events have an exponential distribution with mean 1/λ. If calls come into a police emergency center at the rate of ten per hour, what is the probability that more than 15 minutes will elapse between the next two calls?
Reference
The number of arrivals N at a supermarket checkout counter in the time interval from 0 to t follows a Poisson distribution with mean λt. Let T denote the length of time until the first arrival. Find the density function for T . [Note: P(T > t0) = P(N = 0 at t = t0).]
Questions & Answers
QUESTION:
Problem 169SE
An argument similar to that of Exercise 4.168 can be used to show that if events are occurring in time according to a Poisson distribution with mean λt, then the inter arrival times between events have an exponential distribution with mean 1/λ. If calls come into a police emergency center at the rate of ten per hour, what is the probability that more than 15 minutes will elapse between the next two calls?
Reference
The number of arrivals N at a supermarket checkout counter in the time interval from 0 to t follows a Poisson distribution with mean λt. Let T denote the length of time until the first arrival. Find the density function for T . [Note: P(T > t0) = P(N = 0 at t = t0).]
ANSWER:
Solution:
Step 1 of 2:
Using the exercise 4.168, to show that if events are occurring in time according to a poisson distribution with mean
Then given the inter arrival times between events an exponential distribution with mean
If calls come into a police emergency center at the rate of ten per hour.