Sol-HW2

Sol-HW2 - 1 EE 7615 Solutions Problem Set # 2 1) E [ Y | X...

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Unformatted text preview: 1 EE 7615 Solutions Problem Set # 2 1) E [ Y | X = x ] = Z - yf Y | X ( y | x ) dy E [ Y ] = E [ E [ Y | X ]] = Z E [ Y | X = x ] f X ( x ) dx = Z Z - yf Y | X ( y | x ) f X ( x ) dydx = Z f X ( x ) dx " Z - y 1 2 e- ( y- x ) 2 2 2 dy # = Z - xf X ( x ) dx = EX = m. 2) a) Since R X (0) = 6 6 = 2 X , not a valid autocorrelation function. b) Since R X ( ) 6 = R X (- ) , not a valid autocorrelation function. c) This is a valid autocorrelation function. In fact, as we have seen, it is the autocor- relation function of the random process { X ( t ) } where X ( t ) = 10sin(5 t + ) and where is a random variable uniformly distributed over (0 , 2 ) . d) Since R X ( ) 6 = R X (- ) , not a valid autocorrelation function. 3) a) The power spactral density for the process { X ( t ) } is given by S X ( f ) = Z R X ( ) e- j 2 f d = 2 1 + (2 f ) 2 ....
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This note was uploaded on 03/05/2012 for the course EE 7615 taught by Professor Naragipour during the Fall '11 term at LSU.

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Sol-HW2 - 1 EE 7615 Solutions Problem Set # 2 1) E [ Y | X...

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