Math Problem Statement

For x∈[a,b] , let f(x)=3/4(x−a)(b−x) be a distribution function with a=1 and b=3 , and let f(x)=0 for other values of x . what is the mean

Solution

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Math Problem Analysis

Mathematical Concepts

Probability Distribution
Expected Value
Integration

Formulas

Mean (Expected Value): μ = ∫[a, b] x f(x) dx
Distribution Function: f(x) = 3/4(x - a)(b - x)
Polynomial Expansion: (x - 1)(3 - x) = x^2 - 4x + 3

Theorems

Fundamental Theorem of Calculus

Suitable Grade Level

College-Level (Calculus, Probability Theory)