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convergence of random variables

January 3, 2010

My first class in stochastic processes was tought before we saw a rigorous definition of random variables or their convergence.  This was pretty confusing for me, and so for the first week of presentations I chose to do a “semi-formal” introduction to the concept of random variables (i.e., a step above handwaving but without the formal apparatus of measure theory) suitable for a physics or mathematics student looking for a slightly more formal definition than that given in most introductory textbooks. The various forms of convergence for random variables are introduced, as are the strong and weak versions of the law of large numbers. PDF

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