Math Problem Statement
If the distribution function of x is f(x)= xe^{-x/\lambda} over the interval 0<x<\infty the mean value of x is
(a) λ
(b) 2λ
(c) \frac{\lambda}{2}
(d) 0
Solution
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Math Problem Analysis
Mathematical Concepts
Probability Distribution
Expected Value
Gamma Function
Formulas
Expected Value: \langle x \rangle = \int_0^\infty x f(x) dx
Gamma Function: \int_0^\infty x^n e^{-ax} dx = \frac{n!}{a^{n+1}}
Theorems
Gamma Function Theorem
Expected Value Calculation
Suitable Grade Level
University Level - Statistics/Calculus
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