ORIE 3510/5510 Introduction to Engineering Stochastic Processes I
Summer 2012
ASSIGNMENT 1. Given: July 2, 2012. Due: July 6, 2012. (Revised July 5, 2012)
1. If it is known that in a series of coin tosses, the 4th head occurred on the 12th trial, what is

ORIE3510
Introduction to Engineering Stochastic Processes
Homework 4: Discrete Time Markov Chains Due 2:30pm, February 24, 2010 (drop box)
Spring 2010
Be sure to write your name and section number or day&time on your homework. In all questions, be sure to

ORIE 3510/5510 Introduction to Engineering Stochastic Processes I
Summer 2012
ASSIGNMENT 6. Given: July 24, 2012. Due: Friday, July 27, 2012.
1. In a certain system, a customer must rst be served by server 1 and then by server 2. The service times
at serv

ORIE 3510/5510 Introduction to Engineering Stochastic Processes I
Summer 2012
ASSIGNMENT 5. Given: July 17, 2012. Due: Tuesday, July 24, 2012, at 4:30pm (end of recitation).
1. The Weibull distribution is often used to model failures. The Weibull distribu

ORIE 3510/5510 Introduction to Engineering Stochastic Processes I
Summer 2012
ASSIGNMENT 4. Given: July 13, 2012. Due: July 17, 2012 at 4:30pm after Tuesday recitation
1. Call a transition probability matrix P doubly stochastic if the sum over each column

ORIE 3510/5510 Introduction to Engineering Stochastic Processes I
Summer 2012
ASSIGNMENT 3. Given: July 10, 2012. Due: July 13, 2012.
1. Consider the gamblers ruin chain on states cfw_0, 1, 2, 3, 4 so that if 1 i 3,
pi,i+1 = 0.4,
pi,i1 = 0.6,
but the endp

ORIE 3510/5510 Introduction to Engineering Stochastic Processes I
Summer 2012
ASSIGNMENT 2. Given: July 6, 2012. Due: July 10, 2012.
1. Consider a Markov chain on states cfw_0, 1, 2 with transition matrix
.3 .3 .4
P = .2 .7 .1 ,
.2 .3 .5
and initial proba

ORIE3510
Introduction to Engineering Stochastic Processes
Spring 2016
Homework 7: CTMC
Due 10:30am, Thursday April 28, 2016 (drop box)
Problem 1
Since a failed satellite will never become operational,
P01 (t) = 0
for all t 0
P00 (t) = 1
Let T be the remai

ORIE 3510/5510 Introduction to Engineering Stochastic Processes I
Summer 2012
ASSIGNMENT 7. Given: July 27, 2012. Due: Tuesday, July 31, 2012, at 4:30pm (end of recitation).
1. A store opens at 8am. From 8 until 10 customers arrive at a Poisson rate of fo

ORIE 3510/5510 Introduction to Engineering Stochastic Processes I
Summer 2012
ASSIGNMENT 8. Given: July 31, 2012. Due: Tuesday, August 7, 2012, at 4:30pm (end of recitation).
1. Suppose the lifetime of a high-altitude satellite is an exponential random va

ORIE 3510 Homework 6
Instructor: Mark E. Lewis
due Wednesday March 9, 2012 (ORIE Hallway drop box)
1. One light bulb at Rhodes student lounge has a maximum life of m days. In each day, the bulb
will go crashed with probability p, in which case a new bulb

ORIE3510
Introduction to Engineering Stochastic Processes
Homework 2: Discrete Time Markov Chains Due February 10, 2010 (drop box)
Spring 2010
Be sure to write your name and section number or day&time on your homework. In all questions, be sure to give th

ORIE3510
Introduction to Engineering Stochastic Processes
Homework 3: Discrete Time Markov Chains Due 2:30pm, February 17, 2010 (drop box)
Spring 2010
Be sure to write your name and section number or day&time on your homework. In all questions, be sure to

ORIE3510
Introduction to Engineering Stochastic Processes
Homework 5: Discrete Time Markov Chains Due 2:30pm, March 3, 2010 (drop box)
Spring 2010
Be sure to write your name and section number or day on your homework. In all questions, be sure to give the

ORIE3510
Introduction to Engineering Stochastic Processes
Homework 6: Poisson Processes Due 2:30pm, March 10, 2010 (drop box)
Spring 2010
Be sure to write your name and section number or day&time on your homework. In all questions, be sure to give the jus

ORIE 3510 Homework 1 (Introduction to Probability Theory)
Instructor: Mark E. Lewis
due January 30, 2012 (ORIE Hallway drop box)
This homework assignment is designed to give you some practice in probability. Some of the
concepts should be review, others a

ORIE 3510 Homework 2
Instructor: Mark E. Lewis
due 2PM, Wednesday February 8, 2012 (ORIE Hallway drop box)
1. Give the transition diagrams for the Markov chains with the given transition matrix:
(a)
P=
0.3 0.7
0.5 0.5
(b)
1
0
0
P = 1/2 0 1/2
1/2 1/4 1/4

ORIE 3510 Homework 3
Instructor: Mark E. Lewis
due 2PM, Wednesday February 15, 2012 (ORIE Hallway drop box)
1. Consider the stochastic process
Xn = min(Xn1 , Xn2 ) + n
with X0 = 0, X1 = 0 and n is a random variable taking values 1 and 1 with probability
1

ORIE 3510 Homework 4
Instructor: Mark E. Lewis
due 2PM, Wednesday February 22, 2012 (ORIE Hallway drop box)
1. Show that if state i is recurrent and state i does not communicate with state j , then
pij = 0. (This implies that once a process enters a recur

ORIE3510
Introduction to Engineering Stochastic Processes
Homework 7: CTMCs and the Poisson Process Not to be handed in.
Spring 2010
1. (a) Let Sn be the time that the nth rider departs, then Sn is the sum of n independent exponentials with rate and thus