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Probability and Statistics with Reliability, Queuing, and Computer Science Applications, 2nd Edition by Kishor S. Trivedi

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Chapter 6Stochastic Processes

6.1 Introduction

In the previous chapters we have seen the need to consider a collection or a family of random variables instead of a single random variable. A family of random variables that is indexed by a parameter such as time is known as a stochastic process (or chance or random process).

The values assumed by the random variable c06-math-0005 are called states, and the set of all possible values forms the state space of the process. The state space will be denoted by I.

Recall that a random variable is a function defined on the sample space S of the underlying experiment. Thus the above family of random variables is a family of functions c06-math-0008. For a fixed c06-math-0009 is a random variable [denoted by c06-math-0010] as s varies over the sample space S. At some other fixed instant of time , we have another ...

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