Question: The input to a low pass filter with impulse response h(t) = exp (-10t) u(t) is white, Gaussian noise with single-sided power spectral density of

The input to a low pass filter with impulse response

h(t) = exp (-10t) u(t)

is white, Gaussian noise with single-sided power spectral density of 2 W/Hz. Obtain the following:
(a) The mean of the output.
(b) The power spectral density of the output.
(c) The auto correlation function of the output.
(d) The probability density function of the output at an arbitrary time t₁.

(e) The joint probability density function of the output at times t₁ and t₁ + 0.03 s.

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