%Class for CO907, Tue, Week 1.
%__________________________________________
%Author: Jiarui Cao
%Date: 5 Nov 2013
%Purpose: Visualization of law of large numbers


close all;
clear all;
clc;
clf;
hold on;

%creat some empty arrays
s10 = zeros(200,1);
s100 = zeros(200,1);
s1000 = zeros(200,1);

% run for 200 realizations
for i = 1:200
    rng('shuffle'); %set random number seed. 'shuffle' make sure everytime you have different numbers.
    data = exprnd(1,1000,1); % Generate 1000 exp rnd number with mean 1.
    s10(i)=mean(data(1:10,1));%Take the mean of first 10 data.
    s100(i) = mean(data(1:100,1));%Take the mean of first 100 data.
    s1000(i) = mean(data(1:1000,1));%Take the mean of first 1000 data.
end

%% Plot Histograms

% s(1) = subplot(3,1,1);
% s(2) = subplot(3,1,2);
% s(3) = subplot(3,1,3);
% xcenter=0:0.02:2; %range of histograms
% hist(s(1),s10,xcenter);
% hist(s(2),s100,xcenter);
% hist(s(3),s1000,xcenter);

%%Plot Kernel Densities
 [f1,x1] = ksdensity(s10); 
 plot(x1,f1,'b'); 
 [f2,x2] = ksdensity(s100); 
 plot(x2,f2,'r'); 
 [f3,x3] = ksdensity(s1000); 
 plot(x3,f3,'g'); 
 
 legend('S10','S100','S1000');