ABSTRACT
Some of the most momentous theorems that have a very central role and widespread applications in probability, statistics, and other branches of knowledge are concerning limit theorems. Among those theorems, probably various versions of the laws of large numbers and the central limit theorem are the most prominent ones. In this chapter, we will study those theorems. However, to do so, first we need to study sums of independent random variables and Markov’s and Chebyshev’s inequalities as well as a prerequisite for the study of sums of independent random variables; namely, the celebrated technique of the moment-generating functions.
