Math Problem Statement
find the expected and variance value of RV x
f(x)= ⎩ ⎨ ⎧
2 1 x 0.75 0
if 0<x<1 if 2<x<3 otherwise
Solution
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Math Problem Analysis
Mathematical Concepts
Probability Theory
Expected Value
Variance
Probability Density Function (PDF)
Formulas
Expected value formula: E(X) = ∫ x * f(x) dx
Variance formula: Var(X) = E(X^2) - [E(X)]^2
Condition for valid PDF: ∫ f(x) dx = 1 over the entire range
Theorems
Definition of Expected Value
Definition of Variance
Properties of Probability Density Functions
Suitable Grade Level
Undergraduate Level
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