juniorProbability
What is a random variable in probability theory?
Updated May 17, 2026
Short answer
A random variable is a function that assigns numerical values to outcomes of a random process.
Deep explanation
A random variable maps outcomes from a sample space to real numbers. It allows probabilistic events to be analyzed mathematically. There are two types: discrete (finite/countable values) and continuous (uncountable values). Random variables form the foundation for expectation, variance, and distributions.
Real-world example
Modeling daily stock price changes as a random variable.
Common mistakes
- Thinking a random variable is a variable that changes randomly rather than a function mapping outcomes.
Follow-up questions
- What is the difference between a random variable and a variable in programming?
- What is a discrete random variable?