Math Problem Statement

The formula for the probability density function for the uniform distribution is:

The formula for the probability density function for the uniform distribution is:

for a ≤ x ≤ b

for a ≤ x ≤ b

for a ≤ x ≤ b

for a ≤ x ≤ b

Solution

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Math Problem Analysis

Mathematical Concepts

Probability Theory
Probability Density Functions
Uniform Distribution

Formulas

f(x) = 1 / (b - a) for a ≤ x ≤ b
Expected Value: E(X) = (a + b) / 2
Variance: Var(X) = (b - a)^2 / 12

Theorems

Uniform Distribution Theorem
Properties of Probability Density Functions

Suitable Grade Level

Undergraduate Level