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)