Copyright c 2010 by Karl Sigman
1
Review of the exponential distribution
The exponential distribution has many nice properties; we review them here. A r.v. X has an exponential distribution at rate , denoted by X exp(), if X is nonnegative with c.d.f. F (
Copyright c 2010 by Karl Sigman
1
Continuous-Time Markov Chains
A Markov chain in discrete time, cfw_Xn : n 0, remains in any state for exactly one unit of time before making a transition (change of state). We proceed now to relax this restriction by allo
IEOR 4106
Intro to OR: Stochastic Models
Prof. Mariana Olvera-Cravioto
Assignment #2
February 3, 2016
Page 1 of 1
Assignment #2 - due Wednesday, February 10th, 2016
1. An unbiased die is successively rolled. Let X and Y denote, respectively, the number of
IEOR 4106
Intro to OR: Stochastic Models
Recitation #1
January 29, 2016
Recitation #1
1. We are given three coins: one has heads in both faces, the second has tails in both faces, and
the third has a head in one face and a tail in the other. We choose a c
IEOR 4106
Intro to OR: Stochastic Models
Prof. Mariana Olvera-Cravioto
Assignment #1
January 27, 2016
Page 1 of 1
Assignment #1 - due Wednesday, February 3rd, 2016
1. Stores A, B and C have 50, 75, and 100 employees, and respectively, 50, 60, and 70 perce
Lecture 1
Mariana Olvera-Cravioto
Columbia University
[email protected]
January 20th, 2016
IEOR 4106, Intro to OR: Stochastic Models
Lecture 1
1/14
Introduction
A stochastic process is a collection of random variables, e.g.,
cfw_Xn , n N
or
cfw_Yt
Lecture 2
Mariana Olvera-Cravioto
Columbia University
[email protected]
January 25th, 2016
IEOR 4106, Intro to OR: Stochastic Models
Lecture 2
1/16
Continuous Random Variables
A random variable X is said to be continuous if there exist a nonnegati
Lecture 4
Mariana Olvera-Cravioto
Columbia University
[email protected]
February 1st, 2016
IEOR 4106, Intro to OR: Stochastic Models
Lecture 4
1/18
Conditional expectation and variance
The conditional expectation and the conditional variance of X
Lecture 5
Mariana Olvera-Cravioto
Columbia University
[email protected]
February 3rd, 2016
IEOR 4106, Intro to OR: Stochastic Models
Lecture 5
1/15
Markov chains
Consider a stochastic process cfw_Xn : n = 0, 1, 2, . . . .
Xi S for all i, where S i