Data, mode, and decisions
Instructor’s Manual
Chapter 3
31
Manual to accompany
Data, Models & Decisions: The Fundamentals of Management Science
by Bertsimas and Freund. Copyright
2000, South-Western College Publishing. Prepared by Manuel Nunez, Chapman University.
Chapter 3
I
Chapter Outline
3.1
Continuous Random Variables
3.2
The Probability Density Function
3.3
The Cumulative Distribution Function.
The uniform distribution is introduced.
3.4
The Normal Distribution
General definition of this distribution.
Properties of normal distribution
Presentation
of
several
examples
of
normal
random
variables
and
variables
with non-normal distributions.
3.5
Computing Probabilities for the Normal Distribution
3.6
Sums of Normally Distributed Random Variables
3.7
The Central Limit Theorem
Examples of applications of this theorem.
Discussion on the normal approximation to the binomial
3.8
Summary
II
Teaching Tips
1.
The discussion on the normal approximation to the binomial and the central limit
theorem
can be enhanced by using the Crystal
Ball run option to
show in
class
how the binomial distribution approaches a bell-shaped curve as the sample size
increases. Other distributions might also be used.
2.
A quick in-class survey of the students height and weight can be used to illustrate
how
these
two
measurements
follow
normal
distributions
and
how
common
is
such distribution in nature
III
Answers to Chapter Exercises
3.1
Let X be the site of the traffic incident. X is uniformly distributed between 0 and
30 miles.
(a)
Chapter 3
31
Manual to accompany
Data, Models & Decisions: The Fundamentals of Management Science
by Bertsimas and Freund. Copyright
2000, South-Western College Publishing. Prepared by Manuel Nunez, Chapman University.
Chapter 3
I
Chapter Outline
3.1
Continuous Random Variables
3.2
The Probability Density Function
3.3
The Cumulative Distribution Function.
The uniform distribution is introduced.
3.4
The Normal Distribution
General definition of this distribution.
Properties of normal distribution
Presentation
of
several
examples
of
normal
random
variables
and
variables
with non-normal distributions.
3.5
Computing Probabilities for the Normal Distribution
3.6
Sums of Normally Distributed Random Variables
3.7
The Central Limit Theorem
Examples of applications of this theorem.
Discussion on the normal approximation to the binomial
3.8
Summary
II
Teaching Tips
1.
The discussion on the normal approximation to the binomial and the central limit
theorem
can be enhanced by using the Crystal
Ball run option to
show in
class
how the binomial distribution approaches a bell-shaped curve as the sample size
increases. Other distributions might also be used.
2.
A quick in-class survey of the students height and weight can be used to illustrate
how
these
two
measurements
follow
normal
distributions
and
how
common
is
such distribution in nature
III
Answers to Chapter Exercises
3.1
Let X be the site of the traffic incident. X is uniformly distributed between 0 and
30 miles.
(a)