Math Problem Statement
Suppose X1, X2, . . . , X10 are iid Exp(λ), and we observe the sample mean X¯ = 2.0 What is the maximum likelihood estimate of P(X ≤ 3)?
Solution
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Math Problem Analysis
Mathematical Concepts
Exponential Distribution
Maximum Likelihood Estimation (MLE)
Probability Theory
Formulas
Exponential distribution PDF: f_X(x) = \lambda e^{-\lambda x}
Exponential distribution CDF: F_X(x) = 1 - e^{-\lambda x}
Theorems
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Suitable Grade Level
Advanced Mathematics
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