The bivariate normal distribution is the statistical distribution with probability density function P(x_1, x_2) = 1/(2πσ_1 σ_2 sqrt(1 - ρ^2)) exp[-z/(2(1 - ρ^2))], where z congruent (x_1 - μ_1)^2/σ_1^2 - (2ρ(x_1 - μ_1)(x_2 - μ_2))/(σ_1 σ_2) + (x_2 - μ_2)^2/σ_2^2, and ρ congruent cor(x_1, x_2) = V_12/(σ_1 σ_2) is the correlation of x_1 and x_2 and V_12 is the covariance.

Box-Muller transformation | correlation coefficient--bivariate normal distribution | multivariate normal distribution | normal distribution | Price's theorem | trivariate normal distribution