ORIE 5530: Modeling Under Uncertainty
Fall 2016
Lecture 9 (Tuesday September 20th)
Professor Itai Gurvich
The main new thing we covered in this class was conditional expectations. The way to think about
conditional expectation is (like conditional probabi

ORIE 5530: Modeling Under Uncertainty
Fall 2016
Lecture 9 (Tuesday September 27th)
Professor Itai Gurvich
This notes cover also the content from the previous class, Thursday September 22. In that class we did
two things:
The secretary problem as an examp

ORIE 5530: Modeling Under Uncertainty
Fall 2016
Lecture 8 (Thursday September 15th)
Professor Itai Gurvich
The class today had two main elements
I went over how to simulate multi-variate random variables from independent normal variable. This
material ap

ORIE 5530: Modeling Under Uncertainty
Fall 2016
Lecture 9 (Thursday September 29th)
Professor Itai Gurvich
It will be useful to have a single example to be used throughout.
1
13
2
3
Figure 9.1: A 3-state Markov chain
9.1
Multi-step transition probabilit

an. 11 tVVuAmAL _._- n-_ ,.7, -
12 Let E apd P be mutually exclusive events in the sample space of an experlment.
Suppose that the experiment is repeated until either event E or event F occurs.
What does the sample space of this new super experiment look

ORIE 5530: Modeling Under Uncertainty
Fall 2016
Lecture 7 (Tuesday September 13th)
Professor Itai Gurvich
The class today has two main elements
From discrete random variable to continuous random varaibles: Densities and distributions
Simulation of conti

ORIE 5530: Homework 3. Due October 17
1. This is a simulation question. Consider the Markov chain with the transition probability matrix
0.4 0.38 0.22
P = 0.12 0.7 0.18
0.2 0.5 0.3
a. Simulate and plot a single realization X0 , . . . , Xn of this markov

ORIE 5530: Modeling Under Uncertainty
Fall 2016
Lecture 3 (Tuesday August 30th and Thursday September 1st)
Professor Itai Gurvich
Many thanks to your classmate Jason for sharing his Latex notes. They were used to build
the notes below. The responsibility

ORIE 5530: Homework 1
The homework starts from a question pertaining to events. Question 1 is an exercises in mathematically
expressing complicated events. To be able to compute probabilities of events composed of simpler events,
, we first need to be abl

ORIE 5530: Modeling Under Uncertainty
Fall 2016
Lecture 2 (August 25th)
Professor Itai Gurvich
We spent most of class today on counting. This is useful and fundamental when outcomes are discrete
(such as the number on a die or the number of graphs). Some

ORIE 5530: Modeling Under Uncertainty
Fall 2016
Lecture 3 (August 30th)
Professor Itai Gurvich
In this lecture we introduced probability and defined some basic facts.
So in the previous lecture we said an event is a subset of the sample space. In essence,

ORIE 5530: Modeling Under Uncertainty
Fall 2016
Lecture 3 (Tuesday August 30th and Thursday September 1st)
Professor Itai Gurvich
The class today has three elements
Another version of Chernoff bounds.
An elaborate example of using Chernoff bounds to ana

ORIE 5530: Homework 2. Due Thursday 9/15
1. Simulation Optimization.
A taxi driver in the city of New York wants to decide how much time he should work per day to
maximize his income. Assume that the average money per ride is p dollars. The number of trip

1
Variance
2
Definition 1.1.h Take g (X) =i(X E (X) . Then we can define the variance of a random variable
2
as Var (X) = E (X E (X) .
Fact 1.1. Here are some useful properties of variance:
1. For a constant a, we have
Var (aX) = a2 Var (X) and Var (X + b