Expected value is a fundamental metric in probability theory and decision science defined as the weighted average of all possible outcomes within a random variable's distribution, where each outcome is multiplied by its corresponding probability. Formally represented as $E[X] = \sum (x_i \cdot p_i)$, this concept quantifies the long-run mean return per trial under repeated experimentation conditions. In decision analysis, it serves as an objective criterion for evaluating stochastic games or investments, though practical application requires accounting for non-monotonic utility functions where significant loss risk may render a positive expected value unacceptable despite favorable arithmetic averages.
Prerequisite chain context: requires Random Sampling Techniques in Surveys.