Stat 330 (Spring 2015): Homework 10
Due: April 10, 2015
Show all of your work, and please staple your assignment if you use more than one sheet. Write your name,
the course number and the section on every sheet. Show all work for earning partial credit. Problems marked
with * will be graded and one additional randomly chosen problem will be graded.
1. * Guests of a luxury hotel form a line to use one of 5 terminals located in an internet café in the lobby
area. They arrive at the café at the rate of 10 per hour and spend an average of 20 minutes at a terminal
and then leave. Assuming that both times are distributed exponentially, answer the following questions.
Show work.
(a) Draw a state diagram representing the number of customers using the café.
(b) How many terminals can go down and the system remain stable for servicing customers?
(c) What is the probability that there aren’t any customers in the café?
(d) What is the probability that all terminals are busy?
(e) On the average, how long does a customer stay in the café?
(f) Determine the number of people in the café on the average.
2. (Baron’s book) 8.1
3. (Baron’s book) 8.2
4. A sample of 3 observations of waiting time to access an internet server is x1 = 0.4, x2 = 0.7, x3 = 0.9
seconds. It is believed that the waiting time has the continuous distribution
(
θtθ−1 , 0 < t < 1
f (t) =
0,
otherwise
(a) Find an estimate of the parameter θ using the method of moments.
(b) Find the maximum likelihood estimate of θ.
5. (Baron’s book) 9.1
6. * (Baron’s book) 9.3 (only find maximum likelihood estimator)
1