%  gaussian white noise with var 1
N = 250; % how many samples?

e = randn(N,1); % WN e(t)
e1 = [0 ; e(1:end-1)]; % WN e(t-1)
e2 = [ 0; 0; e(1:end-2)]; % WN e(t-2)
% ---------------------------------

% new stochastic process r. v.
v = e + 2* e1 +e2;

% expected value and variance estimation
EXPv = mean(v);
VARv = var(v);

fprintf(1, ...
    ['Samples: %d \n',...
    'Estimation of exp. value: %f \n',...
    'Estimated variance: %f \n'],...
    N, EXPv, VARv);

% ----------------------------------
figure;
subplot(3,1,1); 
plot(e, '-bo', 'LineWidth',1.5,...
        'MarkerEdgeColor','b',...
        'MarkerFaceColor','b',...
        'MarkerSize',8); grid on
xlabel('time instants'); ylabel('gaussian white noise');

subplot(3,1,2)
plot(v, '-rd', 'LineWidth',1.5,...
        'MarkerEdgeColor','r',...
        'MarkerFaceColor','r',...
        'MarkerSize',8); grid on
xlabel('time instants'); ylabel('stochastic process r. v.');

subplot(3,1,3);
plot(e, '-bo', 'LineWidth',1.5,...
        'MarkerEdgeColor','b',...
        'MarkerFaceColor','b',...
        'MarkerSize',8); hold on;
plot(v, '-rd', 'LineWidth',1.5,...
        'MarkerEdgeColor','r',...
        'MarkerFaceColor','r',...
        'MarkerSize',8);
xlabel('time instants'); grid on