% BIVARIATE NORMAL PROBABILITY DENSITY FUNCTION 

clc;
nobs = 31;
xaxis = (-3:0.2:3)';
yaxis = (-3:0.2:3)';
sigma = [1 .75; .75 1];
binorm = zeros(nobs,nobs);
counter1 = 1;

while counter1 <= nobs
  counter2 = 1;
  while counter2 <= nobs
	x = [xaxis(counter1,1);yaxis(counter2,1)];	
	Q = x'*inv(sigma)*x;
	binorm(counter1,counter2) = ((2*pi)^(-1))*(det(sigma)^(-0.5))*exp(-0.5*Q);
	counter2 = counter2 +1;
  end
  counter1 = counter1 + 1;
end

surf(xaxis',yaxis,binorm);
title(sprintf('Sample Bivariate Normal(0,Sigma) Probability Density Function \n Sigma=[1 0.75; 0.75 1]')); 
xlabel('X2');
ylabel('X1');