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Introduction to Stochastic Processes - Lecture Notes

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Introduction to Stochastic Processes - Lecture Notes (with 33 illustrations)Gordan itkovi Department of MathematicsThe University of Texas at AustinContents1 probability random variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Countable sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Discrete random variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Expectation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Events and probability .

1.1 Random variables Probability is about random variables. Instead of giving a precise definition, let us just metion that a random variable can be thought of as an uncertain, numerical (i.e., with values in R) quantity. While it is true that we do not know with certainty what value a random variable Xwill take, we

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