Generating 2D Joint Gaussian Distribution with MATLAB

You can generate a two-dimensional joint Gaussian distribution through the following steps. First, define the mean vectors and covariance matrices for both Gaussian distributions. The key function for this implementation is MATLAB's `mvnrnd` (multivariate normal random numbers), which generates pseudo-random samples based on specified parameters - this function accepts the mean vector and covariance matrix as inputs and returns sample points following the multivariate normal distribution. Next, utilize MATLAB's visualization functions to display the distribution. The `scatter` function plots the generated samples in a 2D plane, providing a clear visualization of the data distribution pattern. For density representation, employ both `surf` and `contour` functions to create joint distribution density plots - `surf` generates 3D surface plots showing probability density, while `contour` creates 2D contour lines representing equal probability levels. The implementation typically involves calculating the probability density function using `mvnpdf` and then visualizing it through mesh grids created with `meshgrid`. The complete code structure includes parameter initialization, sample generation, density calculation, and multiple visualization techniques to comprehensively demonstrate the joint Gaussian distribution characteristics.