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Unformatted text preview: r , is defined by n n n r S lim ∞ → = Assuming that the random variables X i , i ² 1, are independent, determine r . 4. The continuous parameter random process X( t ) = e A t is a family of exponentials depending on the random variable A. Express the mean & ( t ), the autocorrelation function R( t 1 , t 2 ), and the first-order pdf f( x ; t ) of X( t ) in terms of the pdf f A ( a ) of A. 5. The random variable C is uniform in the interval (0, T ), where T is not random. Find the autocorrelation function of X t if X t = u( t – C). 6. A random process has sample functions of the form ) sin( A ) X( t t ω = where A is a random variable uniform on [-1,1], and & is fixed. a. Find E[X( t )]. b. Find the pdf of ). 2 X( π...
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- Fall '08
- Variance, Probability theory, lim, random variables Xk