%% Ex.01
clear all; close all; clc;

data = load('zad1a.txt');
sigma = std(data);
n = length(data);

chi2bord = chi2inv([0.955 0.045], n-1);
border = sqrt(((n-1)*sigma^2)./chi2bord);

%% Ex.02
clear all; close all; clc;
rng('default');

m = 21;
a = 5;
X = zeros(31,1);
X(1) = 1;

for i=2:31
    X(i) = mod(a*X(i-1),m);
end

subplot(2,1,1); hist(X);
subplot(2,1,2); scatter(X(1:30), X(2:31));
%% Ex.03
clear all; close all; clc;

data = load('zad1b.txt');
data_mean = mean(data);
data_sigma = std(data);

freedom = length(data) - 1;
x = -6:.01:6;
y = tpdf(x,freedom);


hold on; plot(x, y, 'k', 'LineWidth', 1);
t_range = tinv([.975 .025], freedom);
line([t_range(1) t_range(1)],[0 tpdf(t_range(1), freedom)]);
line([t_range(2) t_range(2)],[0 tpdf(t_range(2), freedom)]);

t_test = ((data_mean - 5.6)/data_sigma)*sqrt(length(data));
line([t_test t_test], [0 tpdf(t_test,freedom)], 'Color', 'r');