A Gaussian random process having a mean value of 2 and a variance of 4 is passed through an ideal half-wave rectifier.
a) Let Xp (t) represent the random process at the output of the half-wave rectifier if the positive portions of the input appear in the output. Determine the probability density function of Xp (t) .
b) Let Xn (t) represent the random process at the output of the half-wave rectifier if the negative portions of the input appear in the output. Determine the probability density function of Xn (t) .
c ) Determine the probability density function of Xp (t) Xn (t) .