Multivariate Normal Distribution, Joint Normal Distribution
It is a single distribution and GMM is multiple.
Each random variable normally distributed, at the same time joint multi-variable normally distributed
Covariance Matrix affects exponential part of Probability Density Function
Conditional Mean
가 주어졌을 때 의 평균이 어떻게 이동하는지
generalized form with minus except notation
generalized form with range notation
multi to multi with dimension analysis if we choose k variables for left side
Conditional Variance
generalized form with minus except notation
generalized form with range notation
multi to multi with dimension analysis if we choose k variables for left side
Inverse matrix
If the covariance matrix is singular, it means that the random variables are fully constrained or deterministic, not truly random. For example, if , then the distribution of would collapse into a plane, not a proper 3D Gaussian distribution.