Copyright c 2009 by Karl Sigman
1
Discrete-time renewal processes
Imagine busloads of passengers, where the ith bus contains Hi passengers, and the {Hi } are iid
with pmf
p(k) = P (H = k), k ≥ 1.
(1)
IEOR 6711: Stochastic Models I First Midterm Exam, Chapters 1-2, October 7, 2008
Justify your answers; show your work. 1. A sequence of Events. (10 points) Let cfw_Bn : n 1 be a sequence of events in
IEOR 6711: Stochastic Models I First Midterm Exam, Chapters 1-2, October 10, 2010
Justify your answers; show your work. 1. Exponential Random Variables (23 points) Let X1 and X2 be independent exponen
IEOR 6711, Stochastic Models, I: Final Exam
Fall 2013, SOLUTIONS
There are three questions, each with several parts.
1. Customers Coming to a Group of Automatic Teller Machines
(35 points: 3 points ea
IEOR 6711: Stochastic Models, I Fall 2012, Professor Whitt, Final Exam SOLUTIONS
There are four questions, each with several parts. 1. Customers Coming to an Automatic Teller Machine (ATM) (30 points)
IEOR 6711: Stochastic Models, I Fall 2010, Professor Whitt, Final Exam SOLUTIONS
There are four questions, each with several parts. Question 2 is longer than the others and thus counts more. 1. The Ei
IEOR 6711: Stochastic Models, I Fall 2012, Professor Whitt, Final Exam
There are four questions, each with several parts. 1. Customers Coming to an Automatic Teller Machine (ATM) (30 points) Customers
IEOR 6711: Stochastic Models, I
Fall 2013, Professor Whitt, Final Exam
There are three questions, each with several parts.
1. Customers Coming to a Group of Automatic Teller Machines (35 points)
Custo
IEOR 6711: Stochastic Models, I Fall 2010, Professor Whitt, Final Exam
There are four questions, each with several parts. Questions 2 and 4 are longer than the others and thus count more. 1. The Eight
IEOR 6711: Stochastic Models, I: Final Exam Fall 2007, SOLUTION NOTES
1. The GIN Barbershop (20 points) Ioannis Giannakakis, Gisli Ingimundarson and Behzad Nouri have joined together to form the GIN b
IEOR 6711: Stochastic Models, I Fall 2007, Professor Whitt, Final Exam
1. The GIN Barbershop (20 points) Ioannis Giannakakis, Gisli Ingimundarson and Behzad Nouri have joined together to form the GIN
IEOR 6711: Professor Whitt
Notes on Laplace Transforms and Their Inversion
The shortest path between two truths in the real domain passes through the
complex domain; Jacques Hadamard (1865-1963).
1. B
IEOR 6711: Stochastic Models I, Professor Whitt
Solutions to Homework Assignment 13
Problem 5.12 (a) Since
P0 =
it follows that
1/
=
1/ + 1/
+
N (t)
0
1
=
+
.
t
t
+ +
lim
(b) The expected total time
IEOR 6711: Stochastic Models I
Fall 2013, Professor Whitt
Numerical Transform Inversion Homework: Tuesday, September 10
You have FIVE WEEKS: Due Tuesday, October 15.
1. Write a program implementing th
IEOR 6711: Stochastic Models I
Fall 2013, Professor Whitt
Homework Assignment 13, Tuesday, November 26
Chapter 5: Continuous-Time Markov Chains
Due on Thursday, December 5.
Problems from Chapter 5 of
IEOR 6711: Stochastic Models I, Professor Whitt
Solutions to Homework Assignment 12
Problem 5.3 (a) Let N (t) denote the number of transitions be t. It is easy to show in this case
that
(M t)j
P(N (t)
IEOR 6711: Stochastic Models I SOLUTIONS to First Midterm Exam, October 10, 2010
Justify your answers; show your work. 1. Exponential Random Variables (23 points) Let X1 and X2 be independent exponent
SOLUTIONS to the First Midterm Exam, October 7, 2012 IEOR 6711: Stochastic Models I,
1. Poisson Process and Transforms (30 points) [grading scheme: On all questions, partial credit will be given. Up t
IEOR 6711: Stochastic Models I
First Midterm Exam, Chapters 1-2, October 6, 2013
There are ve questions, each with multiple parts.
Justify your answers; show your work.
1. Random Hats (15 points)
At a
EDU> % Escaping Markov Mouse Example EDU> EDU> % 9 transient states and 3 absorbing states EDU> EDU> % Q from EscapingMouseQ.dat EDU> % R from EscapingMouseR.dat EDU> % program absorbing(Q,R) in absor
IEOR 6711: Stochastic Models I
SOLUTIONS to the Second Midterm Exam, November 17, 2013
1. Random Movement on a Chessboard (25 points)
The king (a chess piece) is placed on one corner square of an empt
IEOR 6711: Stochastic Models I SOLUTIONS to Second Midterm Exam, Chs. 3-4, November 20, 2007
Justify your answers; show your work. 1. Selling Flour: The Grainery. (30 points) The Grainery is a store t
IEOR 6711: Stochastic Models I Second Midterm Exam, Chapters 3 and 4, November 20, 2007
Justify your answers; show your work. 1. Selling Flour: The Grainery. (30 points) The Grainery is a store that s
IEOR 6711: Stochastic Models I
Second Midterm Exam, Chapters 3-4, November 17, 2013
Justify your answers; show your work.
1. Random Movement on a Chessboard (25 points)
The king (a chess piece) is pla
IEOR 6711: Stochastic Models I Second Midterm Exam, Chapters 3-4, November 18, 2012 SOLUTIONS
Justify your answers; show your work. 1. Forecasting the Weather (12 points) Consider the following probab