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A random walk is derived from a sequence of Bernoulli trials. It is used in many fields including thermodynamics, biology, physics, chemistry, and economics where it is used to model fluctuations in the stock market.

Consider a Bernoulli trial in which the probability of success is *p* and the probability of failure is *.* Assume that the experiment is performed every *T* time units, and let the random variable denote the outcome of the *k*th trial. Furthermore, assume that the probability mass function (PMF) of is as follows: ...

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