How does the Box-Muller transform work?
For this project, my goal is to generate Gaussian samples in two dimensions i.e. generating samples whose x and y coordinates are independent standard normals (Gaussian with zero mean and standard deviation of 1). In part 1, I used the inverse Gaussian CDF to generate separately the x and y coordinates from their respective uniform samples (U??? and U???):
Generate x and y coordinates from uniform samples (U??? and U???) using inverse transform sampling
For the Box-Muller transform, I will also start with the same two uniform samples. However, I will transform these uniform samples into the x and y coordinates using much simpler formulas: