Gaussian samples – Part(3)

Generate 1000 Gaussian samples in 2-D using central limit theorem

In short, the central limit theorem allows us to easily generate Gaussian samples in 2-D, whose x and y coordinates are the Gaussian sums of many uniform samples. However, we still need to rescale these x and y coordinates so that they return to standard normal (mean of 0 and standard deviation of 1).

Rescale Gaussian samples

Rescaling the Gaussian samples means we have to subtract each sum by its mean, and divide by its standard deviation.

Gaussian

As a result, the Gaussian samples that represents the x and y coordinates can be normalized as follows:

Please check more detail in the Link

Please also check N-gram language models and Bayesian Statistics.