Math Problem Statement

Solution

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Math Problem Analysis

Mathematical Concepts

Probability Theory
Continuous Random Variables
Expectation
Variance
Integration

Formulas

E[X^2] = ∫ x^2 f(x) dx
Var(X) = E[X^2] - (E[X])^2
f(x) = 2e^(-2x), x > 0

Theorems

Properties of Exponential Distributions
Integration by Parts
Gamma Function

Suitable Grade Level

Undergraduate