# Integer-Valued and Discrete Random Variables

## Abstract

In this chapter, we introduce the concept of random variables and their distributions. In some sense, the entire subject of probability and statistics is about distributions of random variables. Random variables, as the very name suggests, are quantities that vary over time or from individual to individual, and the reason for the variability is some underlying random process. We try to understand the behavior of a random variable by analyzing the probability structure of that underlying random mechanismor process. Random variables, like probabilities, originated in gambling. Therefore, the random variables that come to us *more naturally* are integer-valued random variables; e.g., the sum of the two rolls when a die is rolled twice. Integervalued random variables are special cases of what are known as discrete random variables. We study integer-valued and discrete random variables and their basic properties in this chapter. Random variables with an intrinsically more abstract and complex structure will be studied after we introduce *probability density functions*.

## Keywords

Cumulative Distribution Function Independent Random Variable Sample Space Discrete Random Variable Continuous Random Variable## Preview

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