ISyE 6761 Exam # 2
Fall 2001
Name
Please be neat and show all your work so that I can give you partial credit.
GOOD LUCK.
Question 1
Question 2
Question 3
Total
1
1. (30) Consider a delayed renewal process cfw_ND (t) : t 0 whose rst renewal
time has distr
ISyE 6761 Exam # 2
Fall 2004
Name
Please be neat and show all your work so that I can give you partial credit.
GOOD LUCK.
Question
Question
Question
Question
Total
1
2
3
4
1
1. a. (10) Show that the period of a state in an irreducible Markov chain with
N
ISyE 6761 Final Exam
Fall 2001
Name
Please be neat and show all your work so that I can give you partial credit.
HAPPY HOLIDAYS AND HAVE A WONDERFUL BREAK.
Question
Question
Question
Question
Question
Total
1
2
3
4
5
1
1. (20) Consider a Markov chain with
ISyE 6761 Final Exam
Fall 2004
Name
Please be neat and show all your work so that I can give you partial credit.
HAPPY HOLIDAYS AND HAVE A WONDERFUL BREAK.
Question
Question
Question
Question
Question
Total
1
2
3
4
5
1
1. (20) Consider a Markov chain with
Homework 2
Due February 19, Tuesday
1. If cfw_X (t) : t 0 and cfw_Y (t) : t 0 are independent time-reversible
continuous time Markov chains, show that the process cfw_(X (t), Y (t), t 0
is also time reversible.
2. Consider two queues with Poisson arrivals
Homework 1
Due September 1, Friday
1. a. Let X1 and X2 be independent and identically distributed exponential
random variables with parameter , show that X1 + X2 has the following
density function
f (t) = 2 et t
b. If X and Y are independent exponential r