Math Problem Statement
menghitung E[X], E[X²], dan Var[X] untuk setiap fungsi kepadatan probabilitas (PDF) yang diberikan. f(x) = θx^(θ-1), 0 < x < 1
Solution
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Math Problem Analysis
Mathematical Concepts
Probability Density Function (PDF)
Expected Value (E[X])
Variance (Var[X])
Continuous Random Variables
Integral Calculus
Formulas
E[X] = ∫ x * f(x) dx
E[X²] = ∫ x² * f(x) dx
Var[X] = E[X²] - (E[X])²
f(x) = θ * x^(θ - 1), 0 < x < 1
Theorems
Properties of Continuous Random Variables
Variance Definition
Integral of Powers of x
Suitable Grade Level
Undergraduate Level (Probability and Statistics)
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