Exercise

Calculating probability contours using qmvnorm

The inverse problem to the calculation of cumulative probability is as follows: for a given a probability \(p\) calculate the contour that contains \(p\) proportion of the total volume of the density. This contour is the same as the \(p^{th}\) quantile of the distribution. The qmvnorm() function provides the tools to perform the above calculations.

Instructions

100 XP

Compute the contour for a standard bivariate normal which contains probability \(p=0.9\).
Calculate the contour for a bivariate normal with mean mu.sim and variance-covariance matrix sigma.sim which contains probability \(p=0.95\).