IEOR 6711: Stochastic Models I
Fall 2013, Professor Whitt, Tuesday, September 10
Normal Approximations and the Central Limit Theorem
Time on my hands: Coin tosses.
Problem Formulation: Suppose that I have a lot of time on my hands, e.g., because I
am on t
A Concise Summary
Everything you need to know about exponential and Poisson
Exponential Distribution
Assume that X exp(), by which we mean that X has an exponential distribution with
rate . Then X has mean 1/; i.e., EX = 1/. Also the variance is V ar(X )
IEOR 6711: Stochastic Models I
Fall 2013, Professor Whitt
Topics for Discussion, Thursday, September 26
Innite-Server Queues and Stang
We continued discussing the papers posted last Tuesday. We emphasized Theorem 1 of
the 1993 Physics paper. It describes
IEOR 6711: Professor Whitt, Fall, 2013
Problem for Discussion, Tuesday, September 17
1. Trip to the Post Oce
Five students from IEOR 6711 Jalay Bhandari (B), Hal Cooper (C), Francois Fagan (F),
Irene Lo (L) and Ni Ma (M) simultaneously enter an empty post
IEOR 6711: Stochastic Models I
Professor Whitt, Thursday, September 12
Our Friends: Transforms
1. Our Friends
Identify the following:
(a) generating function (of a sequence)
(b) probability generating function (of a probability distribution or of a random
IEOR 6711: Stochastic Models I
Fall 2013, Professor Whitt
Lecture Notes, Thursday, September 5
Modes of Convergence
1
Overview
We started by stating the two principal laws of large numbers: the strong and weak forms,
denoted by SLLN and WLLN. We want to b
IEOR 6711: Stochastic Models I
Fall 2013, Professor Whitt
Lecture Notes, Tuesday, September 3
Laws of Large Numbers
1
Overview
We start by stating the two principal laws of large numbers: the strong and weak forms, denoted
by SLLN and WLLN. We want to be
IEOR 6711: Stochastic Models I
Professor Whitt
Solutions to Homework Assignment 3
Problem 2.1 The conditions (i) and (ii) of denition 2.1.2 are apparent from the denition 2.1.1.
Hence it is sucient to show that denition 2.1.1 implies the last two conditio
IEOR 6711: Stochastic Models I
Professor Whitt
Solutions to Homework Assignment 2
Problem 1.6 Answer in back.
Problem 1.7 Imagine that there are k buckets and we choose k balls and ll each bucket at the
same time. Set
Ii =
Then X =
k
i=1 Ii .
1
0
if i-th
IEOR 6711: Stochastic Models I
Professor Whitt
Solutions to Homework Assignment 1
The assignment consists of the following ten problems from Chapter 1: Problems 1.1-1.4,
1.8, 1.11, 1.12, 1.15, 1.22 and 1.37. You need not turn in problems with answers in t