Minimize E[|X-b|] where b is a con't rand. var.

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To minimize E[|X-b|], where X is a continuous random variable, the optimal value of b is the median of the distribution of X. The derivation involves analyzing the properties of the absolute value function and its relationship to the distribution of X. The discussion emphasizes the importance of not cross-posting similar questions across multiple forums, as it is against community guidelines. The focus remains on finding the value of b that minimizes the expected absolute deviation from X. Understanding this concept is crucial for statistical analysis and decision-making.
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Homework Statement



Let X be a continuous random variable. What value of b minimizes E(|X-b|)? Give the derivation.

Homework Equations





The Attempt at a Solution

 
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https://www.physicsforums.com/showthread.php?t=527062

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