% 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;