Random variable

Random variable

A random variable is a variable whose possible values are outcomes of a random phenomenon. More specifically, a random variable is defined as a function that maps the outcomes of an unpredictable process to numerical quantities, typically real numbers, which can be either discrete (i.e., taking any of a specified list of exact values) or continuous (i.e., taking any numerical value in an interval or collection of intervals).

Definition

Formally, let S be a sample space — a set of outcomes of a random process. Then a random variable X is a function from S to the real numbers. The technical conditions on the function X are designed to capture the idea that the value of X is determined by the outcome of the random process.

Types of random variables

Random variables can be classified into two broad types:

• Discrete random variables: These are variables that can take on a countable number of values. Examples include the number of heads in a series of coin flips, or the number of students present in a classroom.

• Continuous random variables: These are variables that can take on any value in a given range or interval. Examples include the height of a person, or the time it takes for a computer to process a task.

Probability distribution

The Probability distribution of a random variable is a function that describes the likelihood of each possible outcome. It is defined for every possible outcome in the sample space and satisfies the conditions of a probability measure.

Expectation and variance

The Expected value or expectation of a random variable is a weighted average of all possible values that the random variable can take on, with the weights being the probabilities of these outcomes. The Variance of a random variable is a measure of how much values of the random variable vary around the expected value.

See also

• Probability theory
• Statistics
• Stochastic process
• Probability density function
• Cumulative distribution function

References

Random variable Resources
Need Help Finding a Doctor? Need help finding a doctor or specialist anywhere in the world? Explore our world directory. WikiMD's DocFinder can assist you in locating millions of physicians.	Medical Knowledge Access the latest research - Most recent articles Ongoing trials.

Translate to: East Asian 中文, 日本, 한국어, South Asian हिन्दी, Urdu, বাংলা, తెలుగు, தமிழ், ಕನ್ನಡ,
Southeast Asian Indonesian, Vietnamese, Thai, မြန်မာဘာသာ, European español, Deutsch, français, русский, português do Brasil, Italian, polski