# Eleisha's Segment 17: The Multivariate Normal Distribution

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$\displaystyle \Sigma^{-1} = \left( \begin{array}{ccc} 5 & -1 & 2 \\ -1 & 8 & 1 \\ 2 & 1 & 4 \end{array} \right).$ (Note the matrix inverse notation.)
What are 2-dimensional $\displaystyle \mu$ and $\displaystyle \Sigma^{-1}$ for (a) the distribution on the slice$\displaystyle x_3 =0$ ? (b) the marginalization over $\displaystyle x_3$  ? Hint: The answers are all simple rationals, but I had to use Mathematica to work them out.