Math Problem Statement
Let X be exponential with mean 1/λ; that is, fX (x)= λe^(-λx),0<x<∞ Find Ε[X|X>1].
Solution
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Math Problem Analysis
Mathematical Concepts
Probability Theory
Exponential Distribution
Conditional Expectation
Formulas
f_X(x) = λe^(-λx), 0 < x < ∞ (PDF of exponential distribution)
P(X > 1) = e^(-λ)
Ε[X|X > 1] = 1 + 1/λ
Theorems
Conditional Expectation Formula
Survival Function of Exponential Distribution
Integration by Parts
Suitable Grade Level
Undergraduate
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