# Travis: Segment 19

1. Prove the assertion on lecture slide 5, namely that, for a multivariate normal distribution, the quantity $({\mathbf x-\mathbf\mu})^T{\mathbf\Sigma}^{-1}({\mathbf x-\mathbf\mu})$, where $\mathbf x$ is a random draw from the multivariate normal, is $\chi^2$ distributed.
2. Suppose you measure a bunch of quantities $x_i$, each of which is measured with a measurement accuracy $\sigma_i$ and has a theoretically expected value $\mu_i$. Describe in detail how you might use a chi-square test statistic as a p-value test to see if your theory is viable? Should your test be 1 or 2 tailed?