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  3. Multivariate Probability Distributions in R

Exercise

Cumulative distributions and quantiles of t

In this exercise, you will calculate the probability integrals and quantiles or inverse CDFs of multivariate t-distribution.

Instructions

100 XP
  • Calculate the volume between \(\begin{pmatrix} -5 \\ -5\end{pmatrix}\) and \(\begin{pmatrix} 5 \\ 5 \end{pmatrix}\) for a bivariate t-distribution with location parameter mu.sim and variance-covariance matrix sigma.sim and 5 degrees of freedom.
  • Calculate the equal probability contour for a standard bivariate t-distribution for \(p=.9\). Don't forget to specify tail = "both" to get a two sided contour of the form \(P[-x ≤ X ≤ x] = p.\)