Random variable

Random Variable

A Random Variable (pronounced: /ˈrændəm ˈvɛərɪəbəl/) is a variable whose possible values are numerical outcomes of a random phenomenon. There are two types of random variables, discrete and continuous.

Etymology

The term "Random Variable" was first used in statistics during the 20th century. The word "random" comes from the Old French word "randir" which means to gallop and the Latin word "variabilis" which means changeable.

Definition

A Random Variable is defined as a function that maps the outcomes of unpredictable processes to numerical quantities, typically real numbers. It allows us to work with statistical methods and probability distributions.

Types of Random Variables

There are two types of random variables:

Discrete Random Variable: A variable is a discrete random variable if each of its possible outcomes has a positive probability. Examples include the number of heads in a coin toss, or the number of red cards in a deck of cards.
Continuous Random Variable: A variable is a continuous random variable if it can take on any value in a certain range or interval. Examples include the height of a person, or the time it takes for a computer to process a task.

Related Terms

Probability Distribution: The probability distribution of a random variable is a function that provides the probabilities of occurrence of different possible outcomes.
Expected Value: The expected value of a random variable gives a measure of the center of the distribution of the variable.
Variance: The variance of a random variable is a measure of how much values in the distribution vary from the expected value.