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Unformatted text preview: E [ X 3 ( t )]. 1 6. Let X ( t ) and Y ( t ) be independent, widesense stationary random processes with zero means and the same covariance function C X ( τ ). Let Z ( t ) be deﬁned by Z ( t ) = 3 X ( t )5 Y ( t ) (a) Determine whether Z ( t ) is also widesense stationary. (b) Determine the pdf of Z ( t ) if X ( t ) and Y ( t ) are also jointly Gaussian zeromean random processes with C X ( τ ) = 4 e τ  . (c) Find the joint pdf of Z ( t 1 ) and Z ( t 2 ) in part b. (d) Find the crosscovariance between Z ( t ) and X ( t ). Are Z ( t ) and X ( t ) jointly stationary random processes? (e) Find the joint pdf of Z ( t 1 ) and X ( t 2 ) in part b. Hint : Use auxilliary variables. 2...
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 Winter '10
 khkjk
 Stochastic process, Gaussian Random Process

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