IE230
C
ONCISE
N
OTES
Revised January 9, 2011
Purpose:
These concise notes contain the definitions and results for Purdue University’s
course IE 230, "Probability and Statistics for Engineers, I".
The purpose of these notes is to provide a complete, clear, and concise compendium.
The purpose of the lectures, textbook, homework assignments, and office hours is to
help understand the meanings and implications of these notes via discussion and
examples.
Essentially everything here is in Chapters 2–7 of the textbook, often in the highlighted
blue boxes. Topic order roughly follows the textbook.
Textbook:
D.C. Montgomery and G.C. Runger,
Applied Statistics and Probability for
Engineers
, John Wiley & Sons, New York, 2007 (fourth edition).
Table of Contents
Topic
Pages
Textbook
SetTheory Review
2
None
Probability Basics
3–5
Chapter 2
sample space and events
3
event probability
4
conditional probability, independence
5
Discrete Random Variables
6–8
Chapter 3
pmf, cdf, moments
6
uniform, Bernoulli trials, Poisson process
7
summary table: discrete distributions
8
Continuous Random Variables
9–12
Chapter 4
pdf, cdf, moments, uniform, triangular
9
normal distribution, central limit theorem
10
normal approximations, continuity correction
11
exponential, Erlang, gamma, Weibull
11
Chebyshev’s inequality
11
None
summary table: continuous distributions
12
Random Vectors
13–18
Chapter 5
discrete joint and marginal distributions
13
conditional distributions
14
multinomial distribution
14
continuous distributions
15
conditional distributions
16
covariance, correlation
17
bivariate normal
17
linear combinations, sample mean, central limit theorem
18
Descriptive Statistics
19
Chapter 6
Point Estimation
20–22
Chapter 7
parameter estimator and their properties
20
summary table: point estimators, sampling distribution
21
fitting distributions, MOM, MLE
22
Purdue University
– 1 of 22 –
B.W. Schmeiser
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IE230
C
ONCISE
N
OTES
Revised January 9, 2011
SetTheory Review
A
set
is a collection of items; each such item is called a
member
of the set.
If a set
A
has members
x
,
y
, and
z
, we can write
A
=
{
x
,
y
,
z
}
and, for example,
x
∈
A
.
If a set has members defined by a condition, we write
A
=
{
x

x
satisfies the condition}
.
The vertical line is read "such that".
The largest set is the
universe
, the set containing all relevant items.
The smallest set is the
empty set
(or, sometimes, the
null set
), the set containing no
items; it is denoted by
∅
or, occasionally, by
{}
.
If all members of a set
A
are contained in a set
B
, then
A
is a
subset
of
B
, written
A
⊂
B
.
If two sets
A
and
B
contain the same members, then they are equal, written
A
=
B
.
The
union
of two sets
A
and
B
is the set of items contained in at least one of the sets;
that is,
A
∪
B
=
{
x

x
∈
A
or
x
∈
B
}
.
The
intersection
of two sets
A
and
B
is the set of items contained in both sets; that is,
A
∩
B
=
{
x

x
∈
A
and
x
∈
B
}
. This intersection is also written
AB
.
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 Spring '08
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 Normal Distribution, Probability theory, Purdue University, B.W. Schmeiser

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