Convergence Concepts

Sequences of rvs are important in probability since they reveal interesting behavior essential for mathematical statistics, especially the theory of large sample. The reason is that sequences of rvs or their partial sums enable us to connect patterns of real world data with named distributions. Suppose that \(X_1,\ldots ,X_n\) are IID rvs representing possible values of a population rv X with the same distribution. If we want to infer information on the X’s law, then we might use realizations from each \(X_i\) , whose collection is termed a random sample.