Random Variables and Probability Distributions

Abstract

Following our discussion of probability, this chapter is devoted to random variables and their probability distributions. Understanding random variables is crucial for performing statistical inference, which is discussed in the following chapters. In this chapter, we first talk about defining random variables for some underlying random events (discussed in the previous chapter). For each random variable, we assume a probability distribution, which determines the possible values of the random variable and their corresponding probabilities. The appropriate probability distribution we choose for a random variable depends on its type. We divide random variables into discrete and continuous based on the type values they take and whether these values are countable. We then talk about some commonly used discrete and continuous probability distributions.