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

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 ....
View Full Document

## 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.

### Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online