Let's suppose we have a random variable that maps the results of random experiments to the properties that interest us. The aforementioned random variable measures the likelihood (probability) of one or more sets of outcomes taking place. We call this the probability distribution. Consider probability distribution as the foundation of the concepts we will study in this chapter.
There are three ideas that are of great importance in probability theory—probability space, random variables, and probability distribution. Let's start by defining some of the more basic, yet important, concepts.
The sample space is the set of all the possible outcomes. We denote this with Ω. Suppose we have n likely outcomes—then, we have , where ...
