# Travis: Segment 21

#### To Calculate

**1. Consider a 2-dimensional multivariate normal distribution of the random variable <math>(b_1,b_2)</math> with 2-vector mean <math>(\mu_1,\mu_2)</math> and 2x2 matrix covariance <math>\Sigma</math>. What is the distribution of <math>b_1</math> given that <math>b_2</math> has the particular value <math>b_c</math>? In particular, what is the mean and standard deviation of the conditional distribution of <math>b_1</math>? (Hint, either see Wikipedia "Multivariate normal distribution" for the general case, or else just work out this special case.)**

**2. Same, but marginalize over <math>b_2</math> instead of conditioning on it.**

#### To Think About

**1. Why should it be called the Fisher Information Matrix? What does it have to do with "information"?**

**2. Go read (e.g., in Wikipedia or elsewhere) about the "Cramer-Rao bound" and be prepared to explain what it is, and what it has to do with the Fisher Information Matrix.**