bivariate gaussian

1. Showing Left Side to Right Side.

Let \mathbf x is a (p\times 1) vector, \mathbf\mu_1 is a (p\times 1) vector, \mathbf\mu_2 is a (p\times 1) vector, and \Sigma is a (p\times p) matrix. Now I have to show -\frac{1}{2}(\mathbf x-\mathbf\mu_1)'\Sigma^{-1}(\mathbf x-\mathbf\mu_1)+\frac{1}{2}(\mathbf...
2. Unnormalized multivariate Gaussian?

I'm looking at bivariate Gaussian variables centered on zero. The chi distribution provides moments for a normalized multivariate Gaussian -- i.e., a random variable Y = \sqrt{\sum (\frac{X_i}{\sigma_i}})^2. But I want the variance for the unnormalized vectors Y' = \sqrt{\sum X_i^2}, so I...
3. Bivariate Gaussian - Axses of Ellipses & Prob. Contours

Hi, I found the following link on the web which explains quite well the steps I need to follow to calculate Axes points of probability contours. pdf In slide 21 they have calculated eigenvalue and eigenvector but it is not what I get from Octave or C# libraries. In both cases I get...