Quantitative Analysis

An Introduction

Roy M Chiulli, RoyM Chiulli

• Publisher: Routledge
• Year: 2018
• Print ISBN: 9789056996291
• eBook ISBN: 9781351420617
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

Written in a lecture format with solved problems at the end of each chapter, this book surveys quantitative modeling and decision analysis techniques. It serves to familiarize the reader with quantitative techniques utilized in planning and optimizing complex systems, as well as students experiencing the subject for the first time. It can be used by students of business and public administration without a background in calculus as well as engineers with significant scientific training. It allows the reader to comprehend the material through examples and problems and also demonstrates the value and shortcomings of many methods. Quantitative Analysis: An introduction developed out of the author's experience teaching the material to students at the University of California Los Angeles, California State University, Northridge, and the University of Southern California, Los Angeles.

“Probability is the very guide of life.”

Cicero

1	Probability & Statistics

1.1 Basic Probability

Definition: Probability represents the proportion of the time an outcome will occur in the long run.

Example 1: Consider the toss of a fair die. What is the probability of rolling a “6”?

Answer: There are six equally likely outcomes {1,2,3,4,5,6} and the probability of the outcome “6” is 1/6.

For any given sequence of tosses of the die, the number of “6’s” will not exactly be one-sixth of the total tosses due to the statistical variation (randomness) of the process. However, for a large number of tosses of a fair die (in the long run), the proportion of “6’s” will approach 1/6.

Notes: Two basic axioms of probability are as follows:

• The probability of any single outcome is between 0 and 1, inclusive.

• The sum of the probabilities of all possible outcomes equals 1.

For Example 1, define O_i = The outcome of “i” on a roll of a fair die. Then:

$\begin{array}{ccc}\hfill P(O_1)=P(O_2)=\cdots =P(O_6)& =\hfill & \frac{1}{6}\hfill \\ \hfill P(O_1)+P(O_2)+\cdots +P(O_6)& =\hfill & 1\hfill \end{array}$

Typically, the process being examined will be more complex than the process of rolling a die and be capable of many outcomes. However, the set of all possible outcomes for any process (experiment, system) is called the sample space.

Example 2: The arcade at the Big Top Circus has a game where three darts are thrown at a large number of Blue (B) and Green (G) balloons arranged randomly on a target. Each throw will either a Blue or a Green balloon. Provide the sample space of all possible outcomes for the three throws.

Answer: There are eight possible outcomes:

$\begin{array}{l}\frac{2choices}{(Throw\#1)}\cdot \frac{2choices}{(Throw\#2)}\cdot \frac{2choices}{(Throw\#3)}=8possibleoutcomes(permutations)\\ \begin{array}{ccc}\left\{B\text{,}B\text{,}B\right\}& =& O_1\\ \left\{B\text{,}B\text{,}G\right\}& =& O_2\\ \left\{B\text{,}G\text{,}B\right\}& =& O_3\\ \left\{B\text{,}G\text{,}G\right\}& =& O_4\\ \left\{G\text{,}B\text{,}B\right\}& =& O_5\\ \left\{G\text{,}B\text{,}G\right\}& =& O_6\\ \left\{G\text{,}G\text{,}B\right\}& =...\end{array}\end{array}$

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Series Preface
• Preface
• 1 PROBABILITY & STATISTICS
• 2 DECISION ANALYSIS
• 3 Break-Even Analysis
• 4 INVENTORY DECISION ANALYSIS
• 5 PROJECT MANAGEMENT (PERT/CPM)
• 6 SIMPLE REGRESSION
• 7 FORECASTING
• 8 MULTIPLE REGRESSION
• 9 LINEAR PROGRAMMING (LP)
• 10 QUEUEING
• 11 SIMULATION
• APPENDICES
• Index