Math Problem Statement

Solution

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Math Problem Analysis

Mathematical Concepts

Probability Theory
Moment-Generating Functions (MGF)
Integration

Formulas

MGF M_X(t) = E[e^{tX}] = ∫_{-∞}^{∞} e^{tx} f(x) dx
f(x) = 1/(2√x), for 0 < x < 1

Theorems

Moment-Generating Function Theorem
Fundamental Theorem of Calculus

Suitable Grade Level

University (Undergraduate)