A random variable is a single numerical value that indicates the outcome of a procedure. The concept of random variables is fundamental to the probability theory and was introduced by a Russian mathematician, Pafnuty Chebyshev, in the mid-nineteenth century.

Uppercase letters such as X or Y denote a random variable. Lowercase letters like x or y denote the value of a random variable. If X is a random variable, then X is written in words, and x is given as a number.

For example, let X = the number of heads you get when you toss three fair coins. The sample space for tossing three fair coins is TTT; THH; HTH; HHT; HTT; THT; TTH; HHH. Then, x = 0, 1, 2, 3. X is in words, and x is a number. Notice that for this example, the x values are countable outcomes.

Random variables can be of two types: discrete random variables and continuous random variables.

A discrete random variable is a variable that has a finite quantity. In other words, a random variable is a countable number. For example, the numbers 1, 2, 3,4,5, and 6 on a die are discrete random variables.

A continuous random variable is a variable that has values from a continuous scale without gaps or interruptions. A continuous random variable is expressed as a decimal value. An example would be the height of a student - 1.83 m.

This text is adapted from Openstax, Introductory Statistics, section. 4 Introduction