## Math Problem Statement

Make use of the above result to find the mean, variance, and mode of the beta distribution.

## Solution

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## Math Problem Analysis

### Mathematical Concepts

Beta Distribution

Gamma Function

Probability Distribution

### Formulas

B(a, b) = ∫₀¹ μ^(a-1) (1 - μ)^(b-1) dμ = Γ(a)Γ(b)/Γ(a + b)

Mean: E[μ] = a / (a + b)

Variance: Var[μ] = ab / ((a + b)^2 (a + b + 1))

Mode: (a - 1) / (a + b - 2) for a, b > 1

### Theorems

Beta Function Theorem

Gamma Function Theorem

### Suitable Grade Level

Undergraduate Level

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