Random variables are an important concept in probability theory and statistics. A random variable is a variable whose value is determined by the outcome of a random event. In other words, its value is not known beforehand but depends on the outcome of some underlying probability distribution.

There are two types of random variables: discrete and continuous. Discrete random variables take on a finite or countably infinite set of values, while continuous random variables can take on any value within a specified range.

The probability distribution of a random variable describes the likelihood of each possible value occurring. For a discrete random variable, the probability distribution is given by a probability mass function (PMF), while for a continuous random variable, the probability distribution is given by a probability density function (PDF).

Random variables are used extensively in statistical analysis, where they are used to model uncertain or random processes. They are also used in fields such as finance, engineering, and physics to model and analyze complex systems.