The following commands were run to generate the 1000 values of the random variable X1 with the three covariance
matrices in the problem description:
>> N = 10000;
>> sigma_1=[8000 0; 0 8000];
>> sigma_A=[8000 0; 0 8000];
>> sigma_B=[8000 0; 0 18500];
>> sigma_C=[8000 8400; 8400 18500];
>> gausview(X1A,mu,sigma_A,'Sample X1_A');
>> gausview(X1B,mu,sigma_B,'Sample X1_B');
>> gausview(X1C,mu,sigma_C,'Sample X1_C');
Output 2-D PDF functions using “gausview”:
The symmetry of the above PDF’s is a result of the values in each random process’
values of the 2x2 matrix correspond to the independent X and Y variances.
When these are
and the other
values are zero, the sample values will be equally likely to occur, varying in the X and Y directions equally.
second PDF increased the value of the Y variance.
This results in a wider spread of data values in the Y direction,
however, the PDF contours are still symmetrical about
Finally, the process with a fully populated, non-zero
matrix exhibits variation that occurs along both directions.
When both of the non-diagonal entries are equal, the
variation appears to be along the X-Y diagonal, as show in Figure 3.