function [randomstate, freqstates] = SimulationComplete(P,qzero,nsteps)
% Simulation of nsteps steps of a Markov Chain,
% with transition probability matrix P, and with
% initial probability vector qzero.
% Returns 
%  - the final state (in randomstate)
%  - the relative frequence of each of the three states, as they were generated along the path (in freqstates)
 q = qzero; 
 freqstates = zeros(size(qzero));
 for i = 1 : nsteps
   randomstate = Generate(q);
   freqstates(randomstate) = freqstates(randomstate) + 1;
   q = P(:,randomstate);
 end
 freqstates = freqstates/nsteps;
end