% L3B demo
% Roll a fair 6-sided die n times (default n=6).
% Show two plots:
% Left, GENERATING distribution (of the probabilities)
% Right, EMPIRICAL distribution (from the observed counts)
%
% Optionally, use a particular nonuniform generating distribution.
%
function L3Bdicedemo(n, unfair)

  if nargin<1, n=6; end
  if nargin<2, unfair=false; end

  if unfair
    % A slightly unfair die that favors 1 and 6
    p = [.20 .15 .15 .15 .15 .20];
  else
    p = ones(1,6) / 6;
  end

  x = randsample(1:6, n, true, p);
  nk = hist(x, 1:6);
  emp_p = nk/sum(nk);
  
  % Find largest probability in either plot
  % so we can ensure same scaling
  maxp = max(max(p),max(emp_p));
  
  subplot(1,2,1)
  bar(1:6, p)
  title('Generating distribution')
  set(gca, 'ylim', [0 maxp+0.05]);
  
  subplot(1,2,2)
  bar(1:6, emp_p)
  title(sprintf('Empirical distribution from n=%d', n))
  set(gca, 'ylim', [0 maxp+0.05]);
end