hw8_rp - Consider the random process W ( t ) = Xcos (2 f t...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
EE 351K Probability, Statistics, and Random Processes SPRING 2009 Instructor: Vishwanath sriram@ece.utexas.edu Homework 8 (Due 04/15/2009 in class) Problem1 The count of students dropping the course “Probability and Stochastic Processes” is known to be a Poisson process of rate 0 . 1 drops per day. Starting with day 0 , the first day of the semester, let D ( t ) denote the number of students that have dropped after t days. What is p D ( t ) ( d ) ? Problem 2 For an arbitrary constant a , let Y ( t ) = X ( t + a ) . If X ( t ) is a stationary random process, is Y ( t ) stationary? Problem 3 Let X ( t ) be a stationary continuous time random process. By sampling X ( t ) every Δ seconds, we obtain the discrete time random sequence Y ( n ) = X ( n Δ) . Is Y ( n ) a stationary random sequence? Problem 4
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Consider the random process W ( t ) = Xcos (2 f t ) + Y sin (2 f t ) where X and Y are uncorrelated random variables each with expected value and variance 2 . Find the autocorrelation R W ( t, ) . Is W ( t ) wide sense stationary? Problem 5 X ( t ) is a wide sense stationary random process with average power equal to 1 . Let denote a random variable with uniform distribution over [0 , 2 ] . such that X ( t ) and are independent. a) What is E [ X 2 ( t )] ? b) What is E [ cos (2 f c t + )] ? c) Let Y ( t ) = X ( t ) cos (2 f c t + ) . What is E [ Y ( t )] ? d) What is the average power of Y ( t ) ?...
View Full Document

Ask a homework question - tutors are online