13 17.7 Exercises Ensemble Ensernble t Ensenihle 5: from Figwe 17.1 Exercise 17.2 Discuss which of L21e eiisenibks from Exercise 17.1 could be: a) weak stationary, J ) wcak ergodic Exercise 17.3 Corisiclrr a xandom process ~ ( ta t) the output of i - ~CD-player where (lie sample fiinctioiis are prodiicrd 1-y someone coritiriiially rcpeating a t m serond section from R rock C n Assimic that it is tlrr idcd case in which this has been happciiiing fbr RII irifiriite time aid t he CII-player will go on playiirg infinitely - a) Ilow large are E(r(t)} and x z ( t ) iintler the assimiptiori that the outpiat, has no DC c*omponent'! b) TJsing the first-order expected values, discuss whet her the process could be stalionwy r) TJsing the first-orrlrr expected valiies, discuss whether the proccm coiild be ergodic Exercise 19.4 Take two uiicorrrlatbdraildoin processes z l ( t )R I I J~Z ( ~ ) where p L 1= 2, p L = 0, E{.c;(t)) = and E { z ; ( t ) }= Calculate the averages p g ( t )n$(t) , E ( y L ( f ) }For the rmdoin process y ( t ) = xl(i) rZ(tf + Exercise 17.5 Find (,hevariance of v ( t ) = r(t)i-g(t), wliere x ( t ) is a random signal with varianw = 10 aiid y(t) is any delerriiiriistic signal Exercise 17.6 The ergotiic raritlom process x ( t ) has p, = id nz = Calrxlate pg(t),o;(t), E { g ( t ) and } v,(t) for ~