Math Problem Statement
- The joint density function of the two continuous random variables X and Y is ๐๐ฅ,๐ฆ (๐ฅ, ๐ฆ) = { 6๐ฅ, 0 < ๐ฅ < ๐ฆ < 1 0 ๐๐กโ๐๐๐ค๐๐ ๐ 1-a) Find ๐๐ฅ (๐ฅ) 1-b) Find ๐ธ(๐ฆ|๐ฅ)
Solution
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Math Problem Analysis
Mathematical Concepts
Joint Density Function
Marginal Distribution
Conditional Expectation
Formulas
f_X(x) = โซ f_{X,Y}(x, y) dy
f_{Y|X}(y|x) = f_{X,Y}(x, y) / f_X(x)
E(Y|X=x) = โซ y * f_{Y|X}(y|x) dy
Theorems
Law of Total Probability
Conditional Probability
Suitable Grade Level
University Level (Statistics/Probability)
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