Joint Distributions - Interactive Visualization

Joint distributions capture the relationship between two random variables. The bivariate normal is parameterized by means μ_x, μ_y, variances σ²_x, σ²_y, and correlation ρ. When ρ=0, the variables are independent - the joint is just the product of marginals. As |ρ| increases, knowing X tells you a lot about Y. This visualization shows the density heatmap, marginals as side plots, and conditional distribution as a slice.

• See bivariate normal density heatmap with adjustable μ, σ, ρ
• Watch marginal distributions change on the side panels
• Drag conditional slice x₀ to see conditional distribution P(Y|X=x₀)
• See how ρ controls the shape from circular (ρ=0) to diagonal (|ρ|→1)
• Foundation for multivariate Gaussians, Gaussian processes, and factor models

Part of the EngineersOfAI Interactive 3D - free interactive visualizations covering every major concept in machine learning and AI engineering. Hover any element for a plain-English explanation. No code required.