In this chapter, we learn about random variables on a countable space and their distributions. As measures of location and spread, we introduce their mean and variance. The random variables on the countable space will be referred to as discrete random variables. We present the most important discrete random variables used in finance and their probability distribution (also called probability law):
The operators used for these distributions will be derived and explained in Appendix C of this book. Operators are concise expressions that represent particular, sometimes lengthy, mathematical operations. The appendix to this chapter provides a summary of the discrete distributions covered.
In order to understand the distributions discussed in this chapter, we will explain the general concept of a discrete law. Based on the knowledge of countable probability spaces, we introduce the random variable on the countable space as the discrete random variable. To fully comprehend the discrete random variable, it is necessary to become familiar with the process of assigning probabilities to events in the countable case. Furthermore, the cumulative distribution function will be presented as an important representative of probability. It is essential to understand the mean and variance parameters. Wherever appropriate, we draw analogies to descriptive statistics for a facilitation ...