juniorProbability
What is probability distribution and why is it important?
Updated May 17, 2026
Short answer
A probability distribution describes how probabilities are assigned to values of a random variable.
Deep explanation
A distribution defines the likelihood of all possible outcomes. Discrete distributions use PMF, while continuous distributions use PDF. It fully characterizes a random variable and allows computation of expectation, variance, and probabilities over intervals.
Real-world example
Modeling customer wait times in a queueing system.
Common mistakes
- Confusing probability distribution with a single probability value.
Follow-up questions
- What is PMF vs PDF?
- Can a distribution be unknown?