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Unformatted text preview: 2 2 1 sin ( T / 2) E[S ] S ( ) 2 sin ( T / 2) n d n  = & (multiplier)  + X( t ) Gain 2 1 Second Delay Y( t ) Gain 2 Z( t ) 6. Consider a random process X( t ) that assumes the values 1 or 1. Suppose that X(0) = 1 with probability , and that X( t ) changes polarity with each occurrence of an event in a Poisson process of rate & . Find ( i ) the pmf of X( t ), ( ii ) the mean and variance of X( t ), and ( iii ) the autocovariance function of X( t ). 7. Show that the random process X( t ) of Problem 6 is stationary. Then show that X( t ) approaches stationary behavior as t even if P(X(0) = 1) ....
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 Fall '08
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