# Segment 21. Marginalize or Condition Uninteresting Fitted Parameters

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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 **Failed to parse (unknown error): (b_1,b_2)**
with 2-vector mean **Failed to parse (unknown error): (\mu_1,\mu_2)**
and 2x2 matrix covariance **Failed to parse (unknown error): \Sigma**
. What is the distribution of **Failed to parse (unknown error): b_1**
given that **Failed to parse (unknown error): b_2**
has the particular value **Failed to parse (unknown error): b_c**
? In particular, what is the mean and standard deviation of the conditional distribution of **Failed to parse (unknown error): b_1**
? (Hint, either see Wikipedia "Multivariate normal distribution" for the general case, or else just work out this special case.)

2. Same, but marginalize over **Failed to parse (unknown error): b_2**
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.