%% Ex.01
clear all; close all; clc; rng('default');

N = 9999;
MEAN10 = zeros(N,1);
MEAN100 = zeros(N,1);

for i=1:N
    MEAN10(i) = mean(sqrt(2) * randn(10,1) + 4);
    MEAN100(i) = mean(sqrt(2) * randn(100,1) + 4);
end

subplot(1,2,1); hist(MEAN10, 30);
title('MEAN 10');
subplot(1,2,2); hist(MEAN100, 30);
title('MEAN 100');

%% Ex.02
clear all; close all; clc;

N = 9999;
chi = zeros(N,1);
tStud = zeros(N,1);

for i=1:N
    sample = sqrt(2) * randn(10,1) + 4;
    MEAN = mean(sample);
    s = 0;
    for j = 1:10
        s = s + (1/9)*((sample(j)-MEAN)^2);
    end
    chi(i) = (9*s)/2;
    tStud(i) = ((MEAN - 4)/sqrt(s))*sqrt(9);
end

x_axis_chi = 0:0.1:50;
x_axis_t = -4:0.1:4;
subplot(2,2,1); hist(chi, 50);
subplot(2,2,2); plot(x_axis_chi,chi2pdf(x_axis_chi,9));
subplot(2,2,3); hist(tStud, 50);
subplot(2,2,4); plot(x_axis_t,tpdf(x_axis_t,9));

%% Ex.03
close all; clear all; clc; rng('default');

X = sqrt(2)*randn(10,1) + 4;

% A
sigma_A = sqrt(2);
alfa_A = 0.05;
mean_A = mean(X);
n_A = length(X);
norm_inv_A = norminv([alfa_A/2 1-(alfa_A/2)]);
norm_range_A = mean_A + (norm_inv_A .* (sigma_A/sqrt(n_A)));

% B
sigma_B = sqrt(2);
alfa_B = 0.1;
mean_B = mean(X);
n_B = length(X);
norm_inv_B = norminv([alfa_B/2 1-(alfa_B/2)]);
norm_range_B = mean_B + (norm_inv_B .* (sigma_B/sqrt(n_B)));

% C
sigma_C = std(X);
alfa_C = 0.05;
n_C = length(X);
mean_C = mean(X);
norm_inv_C = tinv([1-alfa_C/2 alfa_C/2], 9);
norm_range_C = mean_C + (norm_inv_C .* (sigma_C/sqrt(n_C)));
norm_range_C = sort(norm_range_C,'ascend');
%% Ex.04
clear all; close all; clc; rng('default');

X = sqrt(2)*randn(10,1) + 4;
MEAN = mean(X);
sigma = std(X);
alfa = 0.05;
freedom = length(X) - 1;
chi2_range = chi2inv([1-(alfa/2) alfa/2], freedom);
chi2_range = sqrt((freedom * sigma^2)./chi2_range);

%% Ex.05
close all; clear all; clc;

X = [15.43, 16.92, 14.43, 12.94, 15.92, 17.42, 18.91, 16.92, 14.93, 14.49, 15.92, 15.43];
X = sort(X, 'ascend');
MEAN = mean(X); SIGMA = std(X);
N = length(X);

SREDNI_PRZYROST = SIGMA/MEAN;
ROZSTEP = max(X) - min(X);
alfa = 0.05;
norm_inv = norminv([alfa/2 1-(alfa/2)]);
norm_range = MEAN + norm_inv.*SIGMA/sqrt(length(X));

M = 1000;
values = zeros(M,1);
for i=1:M
    index = randi([1 12],1,1);
    disp(index);
    values(i) = X(index);
end