Question: A sound wave X (t) = cos(wt + 4) is delayed by 7 /(2w) seconds and then added back into the original signal to produce

 A sound wave X (t) = cos(wt + 4) is delayed

A sound wave X (t) = cos(wt + 4) is delayed by 7 /(2w) seconds and then added back into the original signal to produce a composite signal W(t) = cos(wt + () + sin(wt + d). The phase of the wave, &, is the phase at the initial detection. Assume that & is a random variable that follows a continuous uniform distribution over the interval [-7, 7]. Notice that even though d is a random variable it is independent of time (that is, & is a constant with respect to time). What are the mean and variance of W(t)

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