zz-16 - Utah State University ECE 6010 Stochastic Processes...

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Unformatted text preview: Utah State University ECE 6010 Stochastic Processes Homework # 7 Due Friday Nov. 5, 2004 1. Suppose X t , t is a homogeneous Poisson process with parameter λ . Define a random variable τ as the time of the first occurrence of an event. Find the p.d.f. and the mean of τ . 2. Suppose { X t , t R is a w.s.s. random process with autocorrelation function R X (τ ) . Show that if R X is continuous at τ 0 then it is continuous for all τ R . (Hint: Use the Schwartz inequality.) 3. Under the conditions of problem 2, show that for a > 0, P ( X t τ X t a ) 2 ( R X ( ) R x (τ )) a 2 . 4. Suppose A and B are random variables with E [ A 2 ] < and E [ B 2 ] < . Define the random processes X t , t R and Y t , t R by X t A Bt Y t B At , t R . Find the mean, autocorrelation, and cross correlations of these random processes in terms of the moments of A and B . 5. Let p k ( t , s ) X t X s , where X t is a homoegenous Poisson counting process with rate λ ....
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This note was uploaded on 03/01/2012 for the course ECE 6010 taught by Professor Stites,m during the Spring '08 term at Utah State University.

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zz-16 - Utah State University ECE 6010 Stochastic Processes...

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