# Segment 17. The Multivariate Normal Distribution

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Links to the slides: PDF file or PowerPoint file

### Problems

#### To Calculate

1. Calculate the Jacobian determinant of the transformation of variables defined by

2. Consider the 3-dimensional multivariate normal over with and

. (Note the matrix inverse notation.)

What are 2-dimensional and for

(a) the distribution on the slice ?

(b) the marginalization over ?

Hint: The answers are all simple rationals, but I had to use Mathematica to work them out.

#### To Think About

1. Prove the assertions in slide 5. That is, implement the ideas in the blue text.

2. How would you plot an error ellipsoid in 3 dimensions? That is, what would be the 3-dimensional version of the code in slide 8? (You can assume the plotting capabilities of your favorite programming language.)

#### Class Activity

Bill's Mathematica notebook for problem 2 (above). (Download file, rename as MultivarGaussExample.nb, then open in Mathematica.)