A random variable is a fundamental concept in statistics that links the outcomes of random events to numerical values. Unlike traditional variables in algebra, which can only take a single value at a time, a random variable can assume multiple values, each associated with a specific probability. This allows for a more comprehensive analysis of random phenomena.

There are two main types of random variables: discrete and continuous. A discrete random variable can take on a countable number of distinct values, such as the number of heads when flipping a coin multiple times. In contrast, a continuous random variable can take on an infinite range of values, such as the height of individuals in a population. The probability distribution of a random variable describes how probabilities are assigned to its possible outcomes, with discrete random variables defined by a probability mass function and continuous random variables defined by a probability density function ¹²⁴.

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