Consider a linear time-invariant system with two inputs, as depicted in Figure. Let h₁[n] and h₂[n] be the impulse responses from nodes 1 and 2, respectively, to the output, node 3. Show that if x₁[n] and x₂[n] are uncorrelated, then their corresponding outputs y₁[n] and y₂[n] are also uncorrelated.

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y[n] = y, [n] + y2[n] Network