Noise

Instantaneous noise voltage amplitudes are as likely to be positive as negative. When
plotted, they form a random pattern centered on zero. Since noise sources have amplitudes
that vary randomly with time, they can only be specified by a probability density
function. The most common probability density function is Gaussian. In a Gaussian probability
function, there is a mean value of amplitude, which is most likely to occur. The
probability that a noise amplitude will be higher or lower than the mean falls off in a bellshaped
curve, which is symmetrical around the center.
σ is the standard deviation of the Gaussian distribution and the rms value of the noise voltage
and current. The instantaneous noise amplitude is within ±1σ 68% of the time.
Theoretically, the instantaneous noise amplitude can have values approaching infinity.
However, the probability falls off rapidly as amplitude increases. The instantaneous noise
amplitude is within ±3σ of the mean 99.7% of the time. If more or less assurance is desired,
it is between ±2σ 95.4% of the time and ±3.4σ 99.94% of the time.
σ2 is the average mean-square variation about the average value. This also means that
the average mean-square variation about the average value, i2 or e2, is the same as the
variance σ2.
Thermal noise and shot noise have Gaussian probability density functions.
The other forms of noise do not.