Bivariate Normal Distribution 3D Surface and Tangent Plane

This GeoGebra example demonstrates the 3D probability density surface of a bivariate normal distribution and its geometric features. Core mathematical concepts include multivariate normal distribution, covariance matrix, mean vector, probability density function, maximum point on the surface, and tangent plane. Construction details: using GeoGebra commands, parameters p (correlation coefficient), σ_1, σ_2 (standard deviations), μ_1, μ_2 (means), Coeff (normalization coefficient), Denom (denominator expression), d and b (for constructing the tangent plane) are created, along with Maximum and Max to compute the surface maximum, and text1 to text4 for labeling key points and formulas. This example is suitable for university-level probability and statistics, multivariate analysis, or advanced calculus courses to understand the shape of bivariate normal distributions, parameter effects, and the geometric meaning of tangent planes. It can also be used for classroom demonstrations or student exploration.