clear
fprintf( '\n\nEx. 1\n  x=pi*r^2\n  r0=15.0, sr=1.0\n' )
r0 = 15;
sr = 1;
N = 1e4;
x = zeros( N, 1 );
for i = 1:N
  r = r0 + sr*randn;
  x(i) = pi * (r^2);
end

fprintf( 'sx = %.5f \n', std(x) );
fprintf( 'xm = %.5f \n', mean(x) );
fprintf( 'sxm= %.5f \n', std(x)/sqrt(N) );

% ---------------------------
clear
fprintf( '\n\nEx. 2\n  y=sin(alfa)\n  alfa0=85, salfa=10 (em graus)\n' )
alfa0 = 85;
s_alfa = 10;
N = 1e4;
y = zeros( N, 1 );
for i = 1:N
  alfa = alfa0 + s_alfa*randn;
  y(i) = sin( alfa*(pi/180) );
end

fprintf( 'sy = %.5f \n', std(y) );
fprintf( 'ym = %.5f \n', mean(y) );
fprintf( 'sym= %.5f \n', std(y)/sqrt(N) );


% ---------------------------
clear
fprintf( '\n\nEx. 3\n  z=d^3\n  d0=5.0, sd=1.0\n' )
d0 = 5;
sd = 1;
N = 1e4;
d = d0 + sd *randn(N,1);
z = d.^3;
fprintf( ' sz = %.5f \n', std(z) );
fprintf( ' zm = %.5f \n', mean(z) );
fprintf( ' szm= %.5f \n', std(z)/sqrt(N) );

% ---------------------------
clear
fprintf( '\n\nEx. 4\n  w=a/b\n  a0=10.0, sa=2.0\n  b0=20.0, sb=2.0\n' )
a0 = 10;
sa = 2;
b0 = 20;
sb = 2;
N = 1e4;
w = zeros(N,1);
for i=1:N
  a = a0 + sa *randn;
  b = b0 + sb *randn;
  w(i) = a/b;
end
fprintf( ' sw = %.5f \n', std(w) );
fprintf( ' wm = %.5f \n', mean(w) );
fprintf( ' swm= %.5f \n', std(w)/sqrt(N) );

w_a = zeros(N,1);
for i=1:N
  a = a0 + sa *randn;
  w_a(i) = a/b0;
end
fprintf( ' sw_[a] = %.5f \n', std(w_a) );

w_b = zeros(N,1);
for i=1:N
  b = b0 + sb *randn;
  w_b(i) = a0/b;
end
fprintf( ' sw_[b] = %.5f \n', std(w_b) );