(v) Finding ways to improve the system by experimenting with how inputs and
parameter values produce changes in the system. (vi) to aid in making inferences
and speculations on future system behavior.
Figure 11-1.
Replacing complicated system with approximating mathematical model.
The model constructed can be continuous or discrete. By constructing a math-
ematical model one can use a computer to generate thousands of data values rep-
resenting various outputs under a variety of input scenarios and then one can use
statistics on the data values generated to make inferences concerning the behavior
of the real system. For example, Monte Carlo simulations are discrete models where
random numbers are used in specific ways to help simulate the behavior of a sys-
tem. Monte Carlo methods can be used to study a wide variety of things. A small
sampling of disciplines where Monte Carlo techniques are employed are the study
areas of aerodynamics, fluid dynamics, atomic physics, radiation analysis, material
research, oil exploration, and to verify theoretical predictions.
An example of a Monte Carlo method is the calculation of the value of πusing
random numbers. It can be shown that generating enough random numbers and
using them in the proper way, one can calculate πas accurately as you desire.
The Representation of Data
The data from a population can be either discrete or continuous. If Y is a variable
representing the characteristic being sampled and Y can take on any value between
two given values, then Y is called a continuous variable. If Y is not a continuous
variable, then it is called a discrete variable.
