Probability
Theory
Introduction
REAL WORLD
Chaotic Nature (Uncertainty or
Randomness).
Unavailability of Perfect Models.
Unavailability of Perfect Measurement
Techniques.
Probability: Mathematical modeling of
unpredictable
phenomena.
Statistics: Techn

Lecture Notes
If you were to ask ten people to discuss their opinions about governments role and
purpose, odds are good you will get ten different answers. But chances are also good
that all ten people would like to trust their government. Americas forefa

Exam 5
Question 1 of 40
2.5 Points
Dennis Levine was involved in what aspect of the stock trade?
A. Mergers and acquisitions
B. Arbitrage
C. Investment banking p230
D. International finance
Question 2 of 40
2.5 Points
The investigation that snared Dennis

that
N ( A B)
N ( A B)
P( A B)
N (S )
P( A B )
N ( B)
N ( B)
P( B)
N (S )
. The concept of conditional
probability
can facilitate the calculation of P(A), the unconditional or total probability. This is
especially
true when the calculation of P(A) is dif

Denote
D B C.
P( A B C ) P ( A D) P ( A) P ( D) P ( A D) P ( A) P ( B C ) P[ A ( B C )]
P ( A) P ( B ) P (C ) P ( B C ) P[ A ( B C )].
2.
Now, the Venn diagram can be used to analyze the event
3.
From the Venn diagram shown below, the event
1, area 2, an

probability.
I.4. DEFINITION AND INTERPRETATION OF PROBABILITY.
I.4.1. Classical and Empirical Approaches to Define Probability. The
following example illustrates the evolution of the definition of probability. The
classical definition of probability assu

6.
Public opinion polls.
I.2. DEFINITIONS AND TERMINOLOGY.
Experiment
A process that can be repeated an infinite number of times (at least
theoretically).
A process whose outcome is not known in advance with certainty.
All possible outcomes can be spec

1
Engineering Statistics
Wen K. Shieh, Professor
Department of Chemical & Biomolecular Engineering
University of Pennsylvania
Philadelphia, Pa 19104-6393
TABLE OF CONTENTS
2
I.
ELEMENTS OF PROBABILITY.
5
I.1.
I.2.
I.3.
I.4.
I.5.
I.6.
I.7.
Examples of Appl

Descriptive
Statistics
Random Sample of Size n
Hypergeometric
Experiments.
D
N
Lot
Sample of Size n (n < N)
D
N
Random Sample of Size n.
Population
X f ( x) ( , 2 )
X 1 x1
X 2 x2
X n xn
Random Sample of Size n
X 1 x1
X 2 x2
X n xn
E ( X i )
Var ( X i ) 2

Important Random Variables
DISCRETE RANDOM VARIABLES
Binomial, Bernoulli, Geometric, and Negative Binomial.
Hypergeometric (quality control).
Poisson (temporal and spatial events).
CONTINUOUS RANDOM VARIBALES
Uniform (scheduling).
Exponential (lifetime te

Random Variables
A random variable is a variable whose
numerical value
is determined by the
outcome of a random experiment. The random
experiment means that
the equally likely
probability model is applicable.
Random variables are usually denoted by
capita

Lecture Notes
Most of you probably remember domestic diva Martha Stewart being shipped off to what
became dubbed Camp Cupcake. Analyzing her crimes from a monetary standpoint
only, they represent a drop in the white-collar crime bucket. Some feminists arg