Math Problem Statement
The diameter of an electric cable x is a continuous random variable with pdf f(x)=kx(1-x),0≤x≤1
Find the value of a such that p(x<a)=2p(x>a)
Solution
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Math Problem Analysis
Mathematical Concepts
Probability Theory
Continuous Random Variables
Probability Density Function
Cumulative Distribution Function (CDF)
Integral Calculus
Formulas
PDF f(x) = kx(1-x)
CDF F(a) = ∫₀ˣ 6x(1-x) dx
Theorems
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Suitable Grade Level
Advanced Mathematics
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