hw1 - E(Y) and E(Y 2 ). 3. Let X(t) be a stationary real...

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EE 567 Homework No. 1 C. L. Weber August 29, 2007 Due: September 12, 2007 1. Suppose that X(u) is a Gaussian random variable with zero mean and unit variance. Let Y(u) = a X(u) 3 + b a > 0 Determine and plot the pdf of Y(u). 2. The random variable Y(u) is defined as Y ( u ) = X i i = 1 n ! ( u ) where X i (u), i = 1, … n, are statistically independent random variables with X i ( u ) = 1( withprobabilityp ) 0( withprobability (1 ! p )) " # $ a) Determine the characteristic function of Y(u). b) From the characteristic function, determine the moments
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Unformatted text preview: E(Y) and E(Y 2 ). 3. Let X(t) be a stationary real normal (Gaussian) random process with zero mean. A new process is defined by Y(t) = {X(t)} 2 Determine the autocorrelation function of Y(t) in terms of the autocorrelation function of X(t). 4. Gagliardi Problem 1.2 5. Gagliardi Problem 1.3 6 Gagliardi Problem 1.6 7. Gagliardi Problem 1.11 8. Gagliardi Problem 1.16...
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