A part of a communication system consists of an amplifier of effective noise temperature, $$Te = \,\,21\,\,{}^ \circ K\,$$, and a gain of 13 dB, followed by a cable with a loss of 3 dB. Assuming the ambient temperature to be $$300{}^ \circ \,K$$, we have for this part of the communication system,

The variance of a random variable X is $$\sigma _x^2\,.$$ Then the variance of - kx (where k is a positive constant ) is

White Gaussian noise is passed through a linear narrow band filter. The probability density function of the envelope of the noise at the filter output is: