The power spectral density of a real process X(t) for positive frequencies is shown below. The value of $$E\,\left[ {{X^2}\,(t)} \right]$$ and $$E\,\left[ {X\,(t)} \right]$$, respectively, are

If E denotes expectation, the variance of a random variable X is given by

The PDF of a Gaussian random variable X is given by $${p_x}(x) = \,{1 \over {3\sqrt {2\pi } }}\,\exp \,[ - \,{(x - 4)^2}/18]$$.

The probability of the event {X = 4} is

The amplitude spectrum of a Gaussian pulse is