% process(n) generates a sequence of n independent, identically distributed
% random variables and displays various random sequences derived from it.

function [void] = process(n)

clf

m = 10;                                % dependence on the past

Z = rand(n+2*m,1);                     % iid random variables

a = (0.5).^(1:m);                      % smoothing parameters
a = a/sum(a);                          % normalize

b = (0.9).^(1:m);                      % smoothing parameters
b = b/sum(b);                          % normalize

for i=1:n,
  X(i) = max(Z(i+m-4:i+m));            % recent maximum
  W(i) = median(Z(i+m-5:i+m+5));       % median within a window
  Y(i) = a * Z(i+1:i+m);               % smoothed version of past values of Z
  V(i) = b * Z(i+1:i+m);               % smoothed version of past values of Z
end

subplot(5,1,1)

plot(1:n,Z(m+1:m+n),'.','markersize',12);
axis([0 n 0 1]);
title('Values of Z are independent Uniform(0,1) random variables')

subplot(5,1,2)

plot(1:n,X,'.','markersize',12);
axis([0 n 0 1]);
title('Maximum of last 5 values of Z')

subplot(5,1,3)

plot(1:n,W,'.','markersize',12);
axis([0 n 0 1]);
title('Median of nearest 11 values of Z')

subplot(5,1,4)

plot(1:n,Y,'.','markersize',12);
axis([0 n 0 1]);
title('Weakly smoothed version of last 10 values of Z')

subplot(5,1,5)

plot(1:n,V,'.','markersize',12);
axis([0 n 0 1]);
title('Strongly smoothed version of last 10 values of Z')