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Zero mean white Gaussian noise with a two-sided power spectral density of 
is passed through an ideal low pass filter with a cut-off frequency of 2 KHz and a pass band gain of 1, to produce the noise output n(t).
(a) Obtain the total power in n(t).
(b) Find the autocorrelation function 
of the noise n(t) as a function of 
.
(c) Two noise samples are taken at times 
and 
. Find the spacing 
so that the product 
has the most negative expected value and obtain this most negative expected value.
(a) Total Power = 16 W
(b) 
(c) 
(c) 
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