midProbability
What is independence in probability distributions?
Updated May 17, 2026
Short answer
Independence means joint distribution equals product of marginal distributions.
Deep explanation
If X and Y are independent, then P(X,Y) = P(X)P(Y). This implies no information about one variable can be gained from the other. Independence simplifies modeling significantly.
Real-world example
Rolling two separate dice.
Common mistakes
- Assuming zero correlation implies independence.
Follow-up questions
- Does zero correlation imply independence?
- What is conditional independence?