A stationary, Guassian process X (t) with zero and power

A stationary, Guassian process X (t) with zero and power spectral density Sx (f) is applied to a linear filter whose impulse response b (t) is shown in Figure. A sample Y is taken if the random process at the filter at time T.
(a) Determine the mean and variance of Y.
(b) What is the probability density function ofY?