Matlab/Octave demonstration that random noises 
add quadratically, meaning the square root of the sum
of the squares, using the 'randn' (Random Normal) 
and 'std' (standard deviation) functions.

The notation ">>" means the Matab command window
prompt.  Type what follows into your Matlab window.

First, two create normally distributed random
variables, y and z, each with 1,000,000 points,
a mean value of zero, and an average standard 
deviation of 1.0.

>> n=1000000;
z=randn(1,n);
y=randn(1,n);

Then show that the standard deviation of y or z
separately is very close to 1.0.

>> std(z)
ans =
    1.0001

>> std(y)
ans =
    1.0000

Then show that the standard deviation of y+z is
larger that 1.0, and is equal to the square root
of 2.

std(z+y)
ans =
    1.4141

>> sqrt(2)
ans =
    1.4142

Note: the larger the value of n, the closer the
results come to the expected values.


Alternatively, if y has twice the standard 
deviation of z:

n=1000000;
z=randn(1,n);
y=2.*randn(1,n);

Then,

>> std(z)
ans =
    0.9998

>> std(y)
ans =
    2.0008

>> std(y+z)
ans =
    2.2352

which is the square root of 5, because 
1^1 + 2^2 = 5

>> sqrt(5)
ans =
    2.2361