Dan's Segment 21

To Calculate

1. According to wikipedia: The mean is

$\bar{\boldsymbol\mu} = \boldsymbol\mu_1 + \boldsymbol\Sigma_{12} \boldsymbol\Sigma_{22}^{-1} \left( \mathbf{a} - \boldsymbol\mu_2  \right)$

and covariance matrix

$\overline{\boldsymbol\Sigma} = \boldsymbol\Sigma_{11} - \boldsymbol\Sigma_{12} \boldsymbol\Sigma_{22}^{-1} \boldsymbol\Sigma_{21}.$ The standard deviation is the square root of $\boldsymbol\Sigma_{11}$ from the new covariance matrix.

2. In this case, we just eliminate the second column and second row, so the mean $\bar{\boldsymbol\mu}=\boldsymbol\mu_1$ and the standard deviation is the square root of $\boldsymbol\Sigma_{11}$

Class Activity

This was done in class with Tameem and Sean Trettel, and the code can be found on Sean's wiki page. We had issues plotting an error ellipse, but we have confirmed that our hessian is correct so the issue is not a computational one but a graphical one.