Suppose we have which is the standardized version of the multivariate sample data given by .

a. Show that if we take the sample mean vector of , we will get the null vector.

b. Show that the sample variance-covariance matrix of is the sample correlation matrix of .

[Reference: Johnson, Richard A. and Dean W. Wichern. Applied Multivariate Statistical Analysis, 6th edition. New Jersey: Prentice Hall, 2007.]