# Segment 21. Marginalize or Condition Uninteresting Fitted Parameters

#### Watch this segment

(Don't worry, what you see statically below is not the beginning of the segment. Press the play button to start at the beginning.)

{{#widget:Iframe |url=http://www.youtube.com/v/yxZUS_BpEZk&hd=1 |width=800 |height=625 |border=0 }}

The direct YouTube link is http://youtu.be/yxZUS_BpEZk

Links to the slides: PDF file or PowerPoint file

### Problems

#### 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.

### Class Activity

Today we'll do Find the Volcano.