PROBABILITY THEORY AND STOCHASTIC PROCESSES

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Engineering Bot March 13, 2021
Probability Theory is a mathematical model of uncertainty. In these notes, we introduce
examples of uncertainty and we explain how the theory models them.

It is important to appreciate the difference between uncertainty in the physical world
and the models of Probability Theory. That difference is similar to that between laws of
theoretical physics and the real world: even though mathematicians view the theory as
standing on its own, when engineers use it, they see it as a model of the physical world.

Consider flipping a fair coin repeatedly. Designate by 0 and 1 the two possible outcomes of a coin flip (say 0 for head and 1 for tail). This experiment takes place in the physical
world. The outcomes are uncertain. In this chapter, we try to appreciate the probability
model of this experiment and to relate it to the physical reality.