Question

Write out mu and Sigma(matrix) for a 3-variate Normal distribution explicitely.

Im not really sure what to use for the correlation coefficents for each of the values in sigma matrix.

Answer 1

The R code for printing the elements of - matrix and -matrix (covariance matris) of sample 3-variate Normal distribtion is given below.

my.M<- matrix(c(21,16,28), byrow=T, nrow=3, ncol=1)
my.M
my.S <- matrix(c(2,-3,2,-3,6,4,2,4,3), byrow=T, nrow=3, ncol=3)
my.S
my.R <- cov2cor(my.S)
my.R

The output is:

The mean vector is

> my.M
[,1]
[1,] 21
[2,] 16
[3,] 28

The covariance matrix (sigma matrix) is

> my.S
[,1] [,2] [,3]
[1,] 2 -3 2
[2,] -3 6 4
[3,] 2 4 3

The correlation matrix is
> my.R
[,1] [,2] [,3]
[1,] 1.0000000 -0.8660254 0.8164966
[2,] -0.8660254 1.0000000 0.9428090
[3,] 0.8164966 0.9428090 1.0000000