# Random variable

A random variable is a number that depends on chance. Its probability distribution lists every possible value and how likely each one is. The probabilities must add up to 1.

Statistics (university) · Part 03: Random variables and discrete distributions · Card 1 of 8 · Last updated 2026-10-19

## Analogy

A game show wheel: the wheel is the chance process, and the number it lands on is the random variable.

## Example

**Heads in two flips**

X = number of heads
P(X=0) = 0.25 (TT)
P(X=1) = 0.50 (HT, TH)
P(X=2) = 0.25 (HH)
Total = 1.00

## In practice

Counts of customers, the sum of two dice and waiting times are all random variables.

## Practice

### Flashcards

- **What must probabilities of a distribution add up to?** Exactly 1.

## Questions people ask

### What is the difference between a random variable and a normal variable?

In algebra a variable stands for one unknown value. A random variable takes different values on different occasions, each with a set probability. Before you flip the coin you do not know the count of heads, but you know how likely each count is.

### What is the difference between a discrete and a continuous random variable?

A discrete random variable takes countable values, such as 0, 1, 2 goals. A continuous one can take any value in a range, such as a height or a waiting time. Discrete variables use probabilities for each value. Continuous ones use areas under a curve.

## Related concepts

- [Expected value](https://studyvisually.com/learn/science/statistics-university/statistics-university-part-3/statistics-university-part-3-concept-2)
- [Variance of a random variable](https://studyvisually.com/learn/science/statistics-university/statistics-university-part-3/statistics-university-part-3-concept-3)
- [Linear rules for mean and variance](https://studyvisually.com/learn/science/statistics-university/statistics-university-part-3/statistics-university-part-3-concept-4)

Web page: https://studyvisually.com/learn/science/statistics-university/statistics-university-part-3/statistics-university-part-3-concept-1
Study this card in the app: https://studyvisually.com/app/learn?category=statistics-university&card=statistics-university-part-3-concept-1