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Engineers and scientists create 'models' or approximate representations of complex physical situations. Modeling of a physical situation consists of the making of assumptions about the variables and parameters in an observed system and translating these into mathematical relationships. Once obtained, these obviate the need for more experimentation since the models can predict the future of a given system...
...these models are then utilized as sources of valuable information about the future of the particular physical situation being studied. Thus, a model hopefully predicts the future state of the physical situation being studied. Now there are two types of models in the world of engineering. One which is called a 'Deterministic' Model' and another which is known as a 'Probability Model.' The 'Deterministic Model' refers to a system which is exactly represented by the model and thus the outcome of its functioning is perfectly known. However, one or more uncontrolled factors in a system or the imperfection of the components may introduce an acceptable experimental error. We are not concerned with this type of model. The particular type of model that is to be the subject of this discussion is the probability engineering model since this is where the concept of randomness rears its ugly head.
A 'Probability Model' is a model where one does not know the outcome of a monitored process or physical system beforehand. Hence, the outcome of the system as it proceeds forwards in time is unpredictable. The model is created to formulate a mathematical representation that best describes the process being studied. In other words, since the physical situation is non-deterministic or simply put exhibits bad behavior because unexpected results pop up, a 'Probability Model' is created to bound the physical situation over many repetitive trials. This can be accomplished according to the statistician because as the number of trials or repetitions of the physical reality grows, experimental averages consistently tend to particular values. This tendency to approximate a given value is known as 'Statistical Regularity.'
Now suppose one were to drop a die from a height of one foot upon a hard surface as shown in Figure 11. Then it easy to determine the probability of obtaining a particular outcome; according to probability, one has a one in six chance of getting a particular face of the die. Another example of a physical system subject to probability analysis is the modeling of a communications channel as in Figure 12. Packets of voice communication are encoded at a transmitter, sent via a communications channel and decoded correctly at the receiver through a probabilistic decision making process. The decoder processes data so that a zero should be zero and a one should be a one. In this manner, telephonic digital communication speech can be transmitted on your telephone accurately. The process if of course much more complex but that is it in a nutshell.
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