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johnG2011
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Homework Statement
Let X be a continuous random variable. What value of b minimizes E(|X-b|)? Give the derivation.
Minimize E[|X-b|] where b is a con't rand. var.
- Thread starter johnG2011
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SUMMARY
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. This conclusion is derived from the properties of absolute deviation and the definition of the median, which minimizes the expected absolute error. The discussion highlights the importance of understanding the relationship between a random variable's distribution and its median in statistical analysis.
PREREQUISITES- Understanding of continuous random variables
- Knowledge of expected value and its properties
- Familiarity with the concept of median in statistics
- Basic principles of probability theory
- Study the derivation of the median in various probability distributions
- Explore the implications of minimizing absolute deviation in statistical modeling
- Learn about the differences between mean and median in data analysis
- Investigate applications of E[|X-b|] minimization in machine learning
Statisticians, data analysts, students studying probability theory, and anyone interested in the optimization of statistical measures.
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