% MS-E2170 Simulation
% Exercise 1.4: Chi-squared test
%
% From the second lecture:
%   "k should be at least 100"
%   "N/k should be at least 5" 
% => if k = 100, N > 500.
% 
% Created: 2018-02-19 Heikki Puustinen

%% Initialization

% Sample size for sequence of random numbers.
N = 50;

% Number of sub intervals.
k = 9;

% Number of independent sequences of random numbers.
M = 100;

% Initialize variable where the test results are stored.
p = zeros(M,1);

%% Simulation

for ii = 1:M
    % Create random numbers for the ii:th case.
    r = rand(N,1);
    
    % Run the test.
    p(ii) = chitest(r,k);
end

% Calculate the proportion of rejected cases.
y = sum(p < 0.05) / M;

%% Results

fprintf('Proportion of rejected cases: %.3f\n',y)