Additional Topics in Probability

In chapter 2, we looked at the basic concepts of probability calculations, random variables, and their distributions. There are many special distributions that have useful applications in statistics. It is worth knowing the type of distribution that we can expect under different circumstances, because a better knowledge of the population will result in better inferential results. In this chapter, we discuss some of these distributions with some additional distributions presented in Appendix C . We also briefly deal with joint distributions of random variables and functions of random variables. Limit theorems play an important role in statistics. We will present two limit theorems: the law of large numbers and the Central Limit Theorem.