midProbability
What is expectation in probability theory?
Updated May 17, 2026
Short answer
Expectation is the weighted average of all possible outcomes of a random variable.
Deep explanation
The expectation E[X] is computed as Σ xP(x) for discrete variables or ∫ x f(x) dx for continuous ones. It represents the long-run average value if an experiment is repeated infinitely.
Real-world example
Expected return on investment in finance.
Common mistakes
- Assuming expectation must be a possible outcome.
Follow-up questions
- What is linearity of expectation?
- Is expectation always achievable?