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conditional expectation
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conditional expectation

mathematics
Also known as: conditional mean
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Quick Summary

Conditional expectation is a fundamental concept in probability theory that allows us to predict the value of a random variable given knowledge of another related variable. It is denoted as E(Y12|X) and represents the expected value of Y when X is known.3

The primary goal is to find a function H(X) that minimizes the mean square error of prediction, E{[Y \u2212 H(X)]2}. The solution to this problem is the conditional expectation, H(X) = E(Y|X). This concept is crucial in various fields, including statistics and economics, for making informed predictions based on available data.21

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3 Britannica Sources
  1. probability theory - Expected value
  2. probability theory - Variance
  3. probability theory - Conditional expectation and least squares prediction

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