yield the random variable X, and the deviation of X from be due to N independent (uncorrelated) errors.
Hypothetical measurements with only one of these errors present would yield the deviations 
.
If all these differences can be described by distributions with zero means and variances 
then the difference 
follows a distribution of zero mean and variance
( 
Convolution). Expressed in errors rather than variances, one has the rule of quadratic addition of errors:
which can also be written
For errors 
of normal distribution, the total error 
will also have a normal distribution. For large N, the total error will have normal distribution for any distribution of the
( central limit theorem).