(a) Write an algorithm for drawing a pseudo-random sample from a threedimensional multivariate normal distribution ${N}[\mathbf{0},\mathrm{\Sigma }]$ with ${\sigma }_{jj}=1,j=1,2.3$, and covariances ${\sigma }_{12}={\sigma }_{13}={\sigma }_{23}=0.5$. Draw a sample of 1,000 realizations and compare the estimated means and variances with those of the dgp.

(b) Repeat part (a) with the trivariate normal being replaced by a Student's $t$-distribution with five degrees of freedom.