Convergence of Random Variables

The most important aspect of probability theory concerns the behavior of sequences of random variables. This part of probability is called large sample theory, or limit theory, or asymptotic theory. The basic question is this: what can we say about the limiting behavior of a sequence of random variables X1, X2, X3,...? Since statistics and data mining are all about gathering data, we will naturally be interested in what happens as we gather more and more data.