Math Problem Statement
Suppose that X1,X2,…,Xn is a random sample from the exponential distribution with rate λ>0.
Find the MLE for P(X>1) where X is a future sampled value.
Solution
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Math Problem Analysis
Mathematical Concepts
Exponential Distribution
Maximum Likelihood Estimation (MLE)
Probability Theory
Formulas
Exponential distribution PDF: f(x; \lambda) = \lambda e^{-\lambda x}, \quad x \geq 0
MLE for rate parameter: \hat{\lambda} = \frac{n}{\sum_{i=1}^n X_i}
Probability of survival function: P(X > 1) = e^{-\lambda}
Theorems
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Suitable Grade Level
Advanced Undergraduate
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