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spitz
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Homework Statement
I'm trying to find a natural definition for V[X|Y], but I'm not sure what a natural definition is. Any help?
Natural definition for variance?
- Thread starter spitz
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- Definition Natural Variance
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SUMMARY
The discussion centers on the natural definition of variance conditioned on another variable, specifically V[X|Y]. The participants clarify that V[X|Y] represents a random variable, while V[X|Y = y] is a deterministic value derived from the second moment of X, integrated against the probability density function conditioned on Y. The reference to the Wikipedia page on conditional expectation provides additional context for understanding these concepts.
PREREQUISITES- Understanding of variance and conditional variance in probability theory
- Familiarity with probability density functions (pdf)
- Knowledge of random variables and their properties
- Basic comprehension of conditional expectation
- Study the concept of conditional variance in depth
- Review the properties of probability density functions (pdf)
- Explore the relationship between random variables and their expected values
- Examine the Wikipedia page on conditional expectation for further insights
Students and professionals in statistics, data science, or mathematics who are looking to deepen their understanding of variance and conditional probability concepts.
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