Exercise

Using the pmvnorm function

Along with the density of multivariate normals, you often need to calculate the cumulative distributions of multivariate normals to obtain the volume of the density between two specified values. In this exercise, you will use the pmvnrom() function to calculate the cumulative distribution for specified bivariate normals.

Instructions

100 XP

Compute the volume under a standard bivariate normal distribution between \(\begin{pmatrix} -1\\ -1 \end{pmatrix}\) and \(\begin{pmatrix} 1 \\ 1 \end{pmatrix}\).
Calculate the volume between \(\begin{pmatrix} -5 \\ -5\end{pmatrix}\) and \(\begin{pmatrix} 5 \\ 5 \end{pmatrix}\) for a bivariate normal with mean mu.sim and variance sigma.sim.