Begin2.DVI

Chapter 11

Introduction to Probability and Statistics

The collecting of some type of data, organizing the data, determining how some

characteristic of the data is to be presented as well conducting some type of analysis

of the data, all comes under the category of probability and statistics.

Random Sampling

To determine some characteristic associated with a very large group of objects,

called the population , it is impractical to examine every member of the group in

order to perform an analysis of the population. Instead a random selection of data

associated with objects from the group is examined. This is called a random sample

from the population. Populations can be finite or infinite and by selecting a sample

from the population one expects that some characteristics of the population can be

inferred from an analysis of the sample data.

Analysis of the sample data, without trying to infer conclusions about the popu-

lation from which the sample data comes, is called descriptive or deductive statistics.

An analysis of sample data which tries to predict some characteristic of the popula-

tion is called inductive statistics or statistical inference.

Simulations

Consider the figure 11-1 where some complicated system is described by n-input

variables, j-parameter values, k-output variables and m-neglected or unknown vari-

ables. One replaces the complicated system with a model that in some way mimics

or approximates the behavior of the real system. Those quantities that effect the

model but whose behavior the model is not designed to study are called exogenous

variables. These are usually the independent variables such as the input variables

x 1 ,... , x nand parameters p 1 ,... , p jeffecting system behavior. The behavior of those

quantities from the complicated system that the model is designed to study are

called endogenous variables. These are usually the dependent variables such as the

outputs y 1 ,... , ykproduced by the system.

Simulation is the process of designing a mechanical or mathematical model of a

real system and then conducting experiments with this model for various purposes

such as (i) obtaining a better understanding of the system (ii) to help construct

theories for observed behavior (iii) aid in predicting future behavior (iv) to study

how changes in inputs and parameters values effect the behavior of the system