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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dependence and independence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conditional probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Examples.

Discrete random variables are very nice due to the following fact: in order to be able to compute any conceivable probability involving a discrete random variable X, it is enough to know how to compute the probabilities P[X= x], for all x2S. Indeed, if we are interested in figuring out ... Stochastic Processes); ...

  Processes, Discrete, Stochastic, Stochastic processes