Math Problem Statement

Solution

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Math Problem Analysis

Mathematical Concepts

Maximum Likelihood Estimation (MLE)
Probability Density Function
Exponential Distribution

Formulas

f_θ(x) = e^{-(x-θ)} if x > θ; 0 otherwise
θ̂ = min{x₁, x₂, ..., xₙ}

Theorems

Properties of the Maximum Likelihood Estimator
Exponential Distribution Characteristics

Suitable Grade Level

Undergraduate Level (Statistics/Probability)