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 pr
ISyE 6761
H. Ayhan
Stochastic Processes I
Fall 2016
Homework 3
September 9, 2016
Due on Thursday, September 15
1. Consider a Markov chain with state
0.3
P = 0.2
0.2
space S = cfw_0, 1, 2 and
0.3 0.4
0
ISyE 6761
H. Ayhan
Stochastic Processes I
Fall 2016
Homework 1
August 25, 2016
Due on Thursday, September 1
1. Suppose X and Y are independent Poisson random variables with mean
and , respectively. C
ISyE 6761
H. Ayhan
Stochastic Processes I
Fall 2016
Homework 2
September 1, 2016
Due on Thursday, September 8
1. Let cfw_Zn : n 0 be a branching process as discussed in class. Express
Var(Zn ) in term
ISyE 6761
H. Ayhan
Stochastic Processes I
Fall 2016
Homework 5
September 22, 2016
Due on Thursday, September 29
1. Consider the following two Markov chains (from Homework 4) with state
(5)
space S = c
ISyE 6761
R. D. Foley
Stochastic Processes I
Fall 2015
Homework 4
September 11, 2015
Due on Thursday
1. Yash rolls a pair of fair dice: one is green and the other blue.
(a) If at least one of the dice
ISyE 6761
R. D. Foley
Stochastic Processes I
Fall 2015
Homework 2
September 6, 2015
Due on Thursday
1. On page 22 of our text, we have the equation D P ./ where is the probability of extinction starti
ISyE 6761
R. D. Foley
Stochastic Processes I
Fall 2015
Homework 5
September 18, 2015
Due on Thursday
1. Problem 2.15(a).
2. Problem 2.20(a).
3. Let X0 ; X1 ; : : : be a Markov chain with state space f
ISyE 6761
R. D. Foley
Stochastic Processes I
Fall 2015
Homework 2
August 28, 2015
Due on Thursday
1. I. J. Good showed that the number of customers served in a busy period in an
M/G/1 queue is a branc
ISyE 6761
R. D. Foley
Stochastic Processes I
Fall 2015
Homework 1
August 17, 2015
Due on Tuesday, August 25th
1. Suppose that X has a Bernoulli distribution with parameter p where 0 <
p < 1 and that Y
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 (
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 r
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
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
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 p
ISyE 6761
H. Ayhan
Stochastic Processes I
Fall 2016
Homework 4
September 15, 2016
Due on Thursday, September 22
1. Consider the following two Markov chains with state space S = cfw_0, 1, 2, 3, 4, 5.
F