Transcription of Chapter 6 - Random Processes - UAH
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Chapter 6 - Random Processes - UAH
EE385 Class Notes 11/11/2014 John Stensby Updates at 6-1 Chapter 6 - Random Processes Recall that a Random variable X is a mapping between the sample space S and the extended real line R+. That is, X : S R+. A Random process ( stochastic process) is a mapping from the sample space into an ensemble of time functions (known as sample functions). To every S, there corresponds a function of time (a sample function) X(t; ). This is illustrated by Figure 6-1. Often, from the notation, we drop the variable, and write just X(t). However, the sample space variable is always there, even if it is not shown explicitly. For a fixed t = t0, the quantity X(t0; ) is a Random variable mapping sample space S into the real line.
random walk have been studied over the years (i.e., the gambler's ruin, drunken sailor, etc.). At first, a discrete random walk is introduced. Then, it is shown that a limiting form of the random walk is the well-known continuous Wiener process. Finally, simple equations are developed that
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