3.14 Generate 200 random observations from the 3-dimensional multivariate nor-

mal distribution having mean vector μ = (0,1,2) and covariance matrix

Σ =

[1.0 −0.5 0.5]

[−0.5 1.0 −0.5]

[0.5 −0.5 1.0]

using the Choleski factorization method. Use the R pairs plot to graph an

array of scatter plots for each pair of variables. For each pair of variables,

96 Statistical Computing with R

(visually) check that the location and correlation approximately agree with

the theoretical parameters of the corresponding bivariate normal distribution.

3.15 Write a function that will standardize a multivariate normal sample for arbi-

trary n and d. That is, transform the sample so that the sample mean vector

is zero and sample covariance is the identity matrix. To check your results,

generate multivariate normal samples and print the sample mean vector and

covariance matrix before and after stand=ardization.