A multivariate normal distribution in three variables. It has probability density function P(x_1, x_2, x_3) = e^(-w/[2(ρ_12^2 + ρ_13^2 + ρ_23^2 - 2ρ_12 ρ_13 ρ_23 - 1)])/(2sqrt(2)π^(3/2) sqrt(1 - (ρ_12^2 + ρ_13^2 + ρ_23^2) + 2ρ_12 ρ_13 ρ_23)), where w = x_1^2(ρ_23^2 - 1) + x_2^2(ρ_13^2 - 1) + x_3^2(ρ_12^2 - 1) + 2[x_1 x_2(ρ_12 - ρ_13 ρ_23) + x_1 x_3(ρ_13 - ρ_12 ρ_23) + x_2 x_3(ρ_23 - ρ_12 ρ_13)]. The standardized trivariate normal distribution takes unit variances and μ_1 = μ_2 = μ_3 = 0.

bivariate normal distribution | multivariate normal distribution | normal distribution