juniorProbability
What is independence in random variables?
Updated May 17, 2026
Short answer
Random variables are independent if knowing one does not change probability of the other.
Deep explanation
Two variables X and Y are independent if P(X, Y) = P(X)P(Y). This implies no statistical relationship between them. Independence is a stronger condition than zero correlation.
Real-world example
Rolling two separate dice.
Common mistakes
- Confusing independence with uncorrelated variables.
Follow-up questions
- Can variables be uncorrelated but dependent?
- What is joint probability?