1/24/2010
Computer tools
There are many programs available to help
you compute statistics and display your data,
including
Computing Tools for Statistics
Minitab
SPSS
SAS
S+
Larry G Richards
June 2009
(c)lgr
Unit1 Module 4
1
June 2009
Handle large d

2/2/2010
A little Set Theory
To understand the key ideas
of probability theory, we
need the basic concepts and
notation of set theory.
A little Set Theory
Larry G Richards
(c)lgr
1
Set Theory
Nave
Axiomatic
The theory of probability is based
on the latter

1/14/2010
Starting with DATA
Read Chapter 6 of Milton and Arnold
Descriptive statistics
Understanding Data
Measures of location
Measures of dispersion
Pictures of distributions
Larry G Richards
lgr@virginia.edu
lgr2009
Unit 1 Module 2
Frequency (His

Milton and Arnold Chapter 6
Read the entire chapter
Focus on what we have covered in lecture
(Sections 6.2, 6.3, and 6.4)
Complete problems 10 (except part b), 15b,
17, 18, 21.
We will not collect this homework, but I will
post the answers.
MAE/APMA 6

MAE/APMA 6430:
Exercise: problem 7, chapter 3
Probability and Statistics for
Engineers and Scientists
Discrete Random Variables
Larry G. Richards
(a)
1
Exercise: problem 7, chapter 3
3
Note Table 3.13 is badly placed.
It goes with problem 8 not 7.
Since

2/1/2010
On to Probability
APMA 6430:
Probability and Statistics for
Engineers and Scientists
Basic Probability
Larry G. Richards
1
Why do we need to
introduce probability?
Larry G. Richards
2
Set Theory Notation
A fundamental concept for
understanding st

Characteristics of random
variables
APMA/MAE 6430:
Probability and Statistics for
Engineers and Scientists
Function rule:
Continuous Random
Variables
Larry G Richards
Larry G Richards
Standard normal
Weibull
t distribution (Students) (Chapter 8)
F distrib

2/12/2013
APMA MAE 6430
Review for test 1: new rules
Larry G Richards
Module 17a
I listened to the Module and I liked the
coverage and pacing.
So please watch it.
APMA 6430 Test 1
NEW RULES!
I have replaced slide 28 with the NEW
RULES.
APMA 6430 Test 1
NE

4/5/2010
So far
APMA 6430:
Probability and Statistics for
Engineers and Scientists
Estimation
Module 29:
Hypotheses about
Pairs of Variances
Larry G Richards
Pairs of proportions
Pairs of means
With variance known
With variance unknown
Variances known
Var

4/7/2010
Hypothesis testing:
an extended example
APMA 6430:
Probability and Statistics for
Engineers and Scientists
Module 30:
Hypothesis Testing Problems
Larry G Richards
1
Hypothesis testing:
an extended example
3
Hypothesis testing:
an extended example

4/4/2010
MAE/APMA 6430:
Comparing pairs of parameters
Probability and Statistics for
Engineers and Scientists
Module 28:
Hypotheses about
Pairs of Means
Larry G Richards
1
Comparing Pairs of Means
Larry G Richards
2
Comparing Pairs of Means
X1 is Normal (

Hypothesis tests and confidence
intervals in MINITAB
APMA 6430:
Probability and Statistics for
Engineers and Scientists
Module 31:
Hypothesis Tests and Confidence
Intervals in Minitab
Under Stat
Select Basic Statistics
In the second frame, you will see
La

In hypothesis testing, we have
MAE/APMA 6430
Probability and Statistics for
Engineers and Scientists
A model; the population
Parameters
Statistics relevant to each parameter
Sampling distribution for each statistic
Module 27:
Hypotheses about Proportions

3/28/2010
MAE/APMA 6430:
Three Test Situations
Probability and Statistics for
Engineers and Scientists
Situation 1:
Ho: = 5
(exact)
Ha: > 5 (inexact)
Notes on the logic of Hypothesis Testing
and introduction to
the t statistic and distribution
Larry G R

3/28/2010
On your own (from last class)
Chi Square: revisited
Larry G Richards
Suppose
Ho: p = .5
Ha: p = .7
Compute , 1 - , , and 1 - for
0 1 2 3
AR 3 , , ,
5 5 5 5
Larry G Richards
1
On your own Problem:
Larry G Richards
On your own Problem:
For Ho:

3/21/2010
APMA 6430:
Hypothesis tests
Probability and Statistics for
Engineers and Scientists
We will now explore a variety of
hypothesis testing situations:
Hypothesis Testing:
Logic and Examples
Hypotheses
Hypotheses
Hypotheses
Hypotheses
about
about
ab

APMA 6430:
As we shall see
Probability and Statistics for
Engineers and Scientists
Hypothesis testing
and
Introduction to Hypothesis Testing:
The next BIG Topic
Larry G Richards
are closely related topics.
1
Hypothesis testing
Larry G Richards
2
Hypothesi

3/13/2010
APMA 6430
A NEW Sampling Distribution
Probability and Statistics for
Engineers and Scientists
Chi Square: the Sampling
Distribution of the Variance
Chi Square
Larry G Richards
Sampling Distribution of S
1
What is the sampling distribution of
thi

3/12/2010
APMA 6430
Three types of distributions
Probability and Statistics for
Engineers and Scientists
Sampling Distributions
Larry G Richards
1
Population
(theoretical)
Population (model)
Theoretical distribution
(density function)
Sample (data)
An o

APMA 6430
What we have covered so far
Probability and Statistics for
Engineers and Scientists
Data Display
Basic Concepts of Estimation
Data analysis
Larry G Richards
Larry G Richards
Estimation (Chapter 7)
Discrete (Binomial)
Continuous (Normal)
Logic of

3/11/2010
APMA 6430
Interval estimation
Probability and Statistics for
Engineers and Scientists
Interval Estimation:
Confidence Intervals
We want to establish a range
of values of a variable with a
given probability (likelihood)
of capturing (including) t

3/3/2010
APMA/MAE 6430:
The Normal Distribution
Probability and Statistics for
Engineers and Scientists
Characteristics and Uses of the
Normal Distribution
Larry G Richards
1
The Normal Distribution
f Y (y)
Y 2
e
2
is a continuous random
variable.
is s

Characteristics of random
variables
APMA/MAE 6430:
Probability and Statistics for
Engineers and Scientists
Function rule:
Continuous Random
Variables
Larry G Richards
Larry G Richards
Standard normal
Weibull
t distribution (Students) (Chapter 8)
F distrib

2/12/2013
Reviewing what we have
learned so far in APMA 6430
APMA 6430
Review for test 1
Notes and lectures
Larry G Richards
Modules M1 M16 and MINITAB.
Milton and Arnold
lgr
1
lgr
Basic data representation
Measures of dispersion
Mean , Median, Mode
Varia

3/4/2010
Reviewing what we have
learned so far in APMA 6430
APMA 6430
Review for test 1
Notes and lectures
Larry G Richards
Modules M1 M16 and MINITAB.
Milton and Arnold
lgr
1
lgr
Basic data representation
Measures of dispersion
Mean , Median, Mode
Varian

2/22/2010
Karl Pearson
APMA 6430
Moments of Random Variables
Larry G Richards
1
Pearsons Four Parameters
Larry G Richards
Mean= the central value about which the
measurements scatter
2
Pearsons four parameters
Four Parameters:
With four parameters, we can

2/12/2013
APMA MAE 6430
Review for test 1: new rules
Larry G Richards
Module 17a
I listened to the Module and I liked the
coverage and pacing.
So please watch it.
APMA 6430 Test 1
NEW RULES!
I have replaced slide 28 with the NEW
RULES.
APMA 6430 Test 1
NE

2/22/2010
Have your text handy
APMA/MAE 6430:
Probability and Statistics for
Engineers and Scientists
Other Discrete Distributions
Larry G Richards
Milton and Arnold
Chapter 3, Problem 31
Reviews seven common discrete
distributions.
Shows density, mean, a

MAE/APMA 6430:
Exercise: problem 7, chapter 3
Probability and Statistics for
Engineers and Scientists
Discrete Random Variables
Larry G. Richards
(a)
1
Exercise: problem 7, chapter 3
3
Note Table 3.13 is badly placed.
It goes with problem 8 not 7.
Since

2/5/2010
Joint Events
APMA 6430
Joint Events and Bayes Theorem
Larry G Richards
1
Joint Events
3
Example: coin and die
2
How would we represent the
sample space of this experiment?
One way:
1 2 3 4 5 6
H
T
Larry G Richards
4
Example: coin and die
An