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chapter 6 - 1 Define(a stochastic process(b random...

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1. Define (a) stochastic process; (b) random variable; (c) discrete random variable; and (d) probability distribution. (a) A stochastic process is the counterpart to a deterministic process in probability theory. Instead of dealing only with one possible 'reality' of how the process might evolve under time, in a stochastic or random process there is some indeterminacy in its future evolution described by probability distributions. It may also be defined as a statistical process involving a number of random variables depending on a variable parameter (usually time). (b) A random variable is a function, which assigns unique numerical values to all possible outcomes of a random experiment under fixed conditions. (c) A random variable is which can assume only a countable number of distinct values such as 0, 1, 2, 3, ... is called a discrete random variable. (d) Probability distribution of a discrete random variable is a list of probabilities associated with each of its possible values. It is also called probability mass function or simply probability function.
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