A signal, when going through an electronic device, is distorted, which amounts to adding a random distortion error X. Suppose that X is normal with zero mean and a standard deviation of ε. The latter may be viewed as a measure of distortion. Assume that the signal is going through nine consecutive independently functioning devices identical to the device above.
What is the distribution of the total distortion? Is the measure of total distortion (the standard deviation) nine times as large as this measure for one device? Find the probability that the absolute value of the total distortion error does not exceed 6ε.