1. Proof using Cholesky decomposition
Food for Thought Problems
1. T-value is the number of standard deviation from the mean that the given data is on the distribution. This can be a good first estimate of our data with respect to the model. Square of the t-value fits the chi-square distribution
2. Since the extremes can happen on both sides, a two-tailed p-value would be the ideal process. To calculate this, the sum of the square of every <math> (x_i - \mu_i)/\sigma_i </math> can be put into the chi-sq formula.