Math Problem Statement

Solution

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Math Problem Analysis

Mathematical Concepts

Multivariate Normal Distribution
Conditional Probability
Integration

Formulas

Quadratic form in normal distribution: (1/σ11) x1^2 + (σ11/D) (x2 - (σ12/σ11) x1)^2
Conditional density: f(x1, x2) = (1 / √(2πτ)) exp[-(1 / (2τ)) (x2 - (σ12/σ11) x1)^2]
τ = σ22 - σ12^2/σ11

Theorems

Conditional Distribution of Multivariate Normal
Properties of Gaussian Integrals

Suitable Grade Level

Undergraduate