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

The set [0;1] of all real numbers between 0 and 1 is not countable; this fact was first proven by Georg Cantor who used a neat trick called the diagonal argument . 1.3 Discrete random variables

  Introduction, Countable, Stochastic

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