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A stochastic process is a system of countable events, where the events occur according to some well-defined random process. Strictly speaking, a stochastic process is also concerned with the sequence in which the events occur in time, but we shall take the more usual broader definition to include counting systems where the order is of no importance. This section describes four very fundamental stochastic processes: the Binomial, Poisson, Hypergeometric, and Central Limit Theorem (CLT).

 

 

 

 

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This section also discusses a generalization of the Poisson process where the times between events are independent and identically distributed with an arbitrary distribution, a type of randomness known as a renewal process which is often used in modeling equipment reliability, for example.

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Finally, some examples are given of mixture processes. These are random processes where one or more of the defining parameters (like a binomial probability, for example) may itself be a random variable. There are some very useful theoretical results that come out of mixture processes, and in Monte Carlo simulation this is something that do we quite naturally anyway by simply nesting distributions.

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