Lessons in Estimation Theory for Signal Processing, Communications, and Control, Second Edition

Lesson 12 Multivariate Gaussian Random Variables

Summary

This is a transition lesson. Prior to studying the methods for estimating unknown random parameters, we review an important body of material about multivariate (i.e., vector) Gaussian random variables. Most, if not all, of the material in this lesson should be a review for a reader who has had a course in probability theory.

The purpose of this lesson is to collect a wide range of facts about multivariate Gaussian random variables in one place, because they are often needed in the remaining lessons. Two of the most important facts are that (1) the conditional density function for two jointly Gaussian vectors is also Gaussian, and (2) the conditional mean is random.

When you complete this ...