 Bivariate normal distribution

ID: bivariate-normal-distribution

Codex  0 Created 2026-09-24 Updated 2026-09-28

μ_{i}

σ_{i}

ρ

, the standardized quadratic form in the density is

\frac{1}{1 - ρ ^{2}} [\frac{( x _{1} - μ _{1} ) ^{2}}{σ _{1}^{2}} - \frac{2 ρ ( x _{1} - μ _{1} ) ( x _{2} - μ _{2} )}{σ _{1} σ _{2}} + \frac{( x _{2} - μ _{2} ) ^{2}}{σ _{2}^{2}}] .

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