expectation
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An expectation is the long-run average value you'd get if you repeated a random experiment many times and calculated the mean of all the outcomes. It matters because it tells you what to expect "on average" from uncertain situations, making it useful for decision-making and predicting typical outcomes.
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In probability theory, the expected value (also called expectation, mean, or first moment) is a generalization of the weighted average.
The expected value of a random variable with a finite number of outcomes is a weighted average of all possible outcomes. In the case of a continuum of possible outcomes, the expectation is defined by integration. In the axiomatic foundation for probability provided by measure theory, the expectation is given by Lebesgue integration.