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clc;
clear all;
close all;

N = 1000000;
x = randn(1, N);
mu = mean(x);
sigma2 = var(x); 
step = 0.1;
range = -3:step:3; h = histc(x, range);
f = ((1./(sqrt(2.*pi.*sigma2))).*exp((-(range-mu).^2)./(2.*sigma2)));

figure;
plot(range, f, 'b', 'linewidth', 2);
hold on;

simulatedPDF1 = h./(step.*sum(h));
plot(range, simulatedPDF1, '*', 'markersize', 15);

bar(range, simulatedPDF1, 'histc');


title('Gaussian distribution');
xlabel('range');
ylabel('PDF');
legend('Theoretical', 'Simulated', 'Simulated');
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