Math Problem Statement
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Solution
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Math Problem Analysis
Mathematical Concepts
Probability Density Functions
Conditional Probability
Piecewise Functions
Formulas
f_X(x) = x/2 for 0 < x <= 1
f_{Y|X}(y | 0.5) = 2 for 0 < y < 1/2
f_{X|Y}(x | 0.5) = 0.5 for 1/2 < x < 1
Theorems
Basic PDF Properties
Conditional Probability Formula
Suitable Grade Level
Grades 11-12 or Early University Level
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