Math Problem Statement
menghitung E[X], E[X²], dan Var[X] untuk setiap fungsi kepadatan probabilitas (PDF) yang diberikan.b) f(x) = 4e^(-4x), x > 0
Solution
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Math Problem Analysis
Mathematical Concepts
Probability Theory
Expected Value
Variance
Exponential Distribution
Formulas
E[X] = ∫_(-∞)^∞ x f(x) dx
E[X^2] = ∫_(-∞)^∞ x^2 f(x) dx
Var(X) = E[X^2] - (E[X])^2
Theorems
Expected Value of Continuous Random Variables
Variance Theorem
Suitable Grade Level
Undergraduate level (Statistics/Probability Theory)
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