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A stationary, Guassian process X (t) with mean μX and varia

A stationary, Guassian process X (t) with mean μX and varia

A stationary, Guassian process X (t) with mean ÂľX and variance s2X is passed through two linear filters with impulse responses b1 (t) and b2 (t) yielding processes y (t) and Z (t), as shown in Figure.
(a) Determine the joint probability density function of the random variables Y (t1) and Z (t2).
(b) What conditions are necessary and sufficient to ensure that Y (t1) and Z (t2) are statistically independent?

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