Math Problem Statement

Solution

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Math Problem Analysis

Mathematical Concepts

Probability Density Functions
Gaussian Distribution
Integration
Conditional Probability

Formulas

f_X(x) = Cx^2 for 0 ≤ x ≤ 1
f_X(x) = C(2 - x) for 1 < x ≤ 2
Total Probability ∫ f_X(x) dx = 1
Gaussian Distribution PDF: f(x) = (1 / √(2πσ^2)) * e^(-(x - μ)^2 / 2σ^2)

Theorems

Fundamental Theorem of Calculus
Properties of Probability Density Functions
Gaussian Distribution Properties

Suitable Grade Level

Undergraduate (University Level)