% part_b
%
% Finds the limiting distribution for the Markov chain by simulating
% the chain multiple times starting from 1.

function lim_dist = part_b(n,number_of_simulations,time)
% Input Variables
%   n				The size of the state space
%   number_of_simulations	Number of times to simulate chain
%   time			Amount of time to simulate chain

% Initialize 
frequencies = zeros(n,1); % keep track of where chain ends up

for loop1 = 1:number_of_simulations
  x = 1;  % starting state
  u = rand(time,1);  % draw the uniform random variables we will need
  for loop2 = 1:time
    x = part_a(x,u(loop2),n);
  end
  frequencies(x) = frequencies(x) + 1;
end
lim_dist = frequencies / number_of_simulations;