Definition
Expected value sums the products of possible random-variable values and their probabilities. In a finite table, probabilities must be non-negative and sum to one. A continuous model uses the corresponding averaging over a distribution.[1]
Illustrative calculation
If the result is +100 with probability 60% and −200 with probability 40%, the expected value is −20. The positive outcome occurs more than half the time, but its size does not offset the negative outcome. These are fictional conditions, not a forecast for an instrument.
Limitation
Expected value is not the most likely outcome, a guarantee or an estimate of whether a loss can be endured. It depends on the stated probabilities and the completeness of the scenarios. A positive average result also does not mean that the participant has enough capital to survive an adverse sequence. The [expected value of a decision](/guides/expected-value-decisions/) continues the review of assumption robustness and separates monetary expectation from liquidity constraints and the decision-maker’s utility.
Primary material
[1] MIT, Lecture 20: Uncertainty; expected-value formula and the distinction between monetary value and utility. [Lecture 20: Uncertainty](https://ocw.mit.edu/courses/14-01-principles-of-microeconomics-fall-2023/mit14_01_f23_lec20.pdf)