Part VI — Multivariate Probability

Probability for random vectors: covariance and correlation matrices, linear transformations, and the multivariate Gaussian — the machinery portfolio mathematics is built on.

Topics

Topic	Focus
Multivariate Random Variables	Random vectors and their joint behavior
Covariance Matrices	The covariance matrix, positive semidefiniteness, and portfolio variance
Correlation Matrices	Standardized dependence across many assets
Linear Transformations	How mean vectors and covariance matrices transform under linear maps
Multivariate Gaussian Distribution	The joint normal density and its geometry
Conditional Gaussian Distributions	Conditioning a joint normal, the basis of linear prediction