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EE464_Discussion_15_042110

EE464_Discussion_15_042110 - _fl 5535 gigcushog#15 2...

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Unformatted text preview: _fl 5535!; gigcushog #15 , . 2 samnehndls oosfeeo. (700 .thu {705x649 m Assuqnmm~ z Vii '5 \ alum? mdusfic. 16$ a). ?$+00ham€ -—7 P" smmmé ~ H ' UMMj P21 g v, ( Pi.) : , P1 :1 r“ 7 1 a ._P!_\ *a 1m 5th ' a i... 14 1’ is d 0 “M3 511 C k 0‘ S“ & WWW 'M...__..__._ (9.11%. erAne); W(A|%)W(B). “JELan’ Xn ‘15:] :Xn,'_ . . . . [tpiXMAEZL - - __r__-.-.'._‘.'.X.r__:|_ __._..__________ C\__E_§l§.2€.d s-d' 0% pemknr. 0 Show that {8"}?le is a Markov chain. 0 Is it a homogeneous Markov chain? 0 If it is, find the transitional probabilities. o How many classes this chain has? 0 Is the chain recurrent? o Is the chain non—null? For the last two problems, you need to consider all possible values of p, q. 5. If in the last problem, the next state function is defined as Sn“ = n+1 = max{0, Sn+3X,,} and p = q = %. Repeat all questions. 6. Suppose the transitional probability matrix of a homogeneous Markov chain is given as follows: . TUC‘U 0?" , 0.6 0.2 = ~\‘-~ IS 1"“ l ' \l | P 0 0 0 2‘ ' C‘ ’ 0 0 . 0 0 . l 1. ”S 06 0.2 ’l 3 bl 5(5'1 — i U (' ' m+6 0 0 :75 {Wm WM 0 0 - P= 0 0 Mi 6 ' '2 WM W079 - 0 0.5 “We 0 0.5 0 0 Classify the states into equivalent classes. Find out the properties of each class. Whether they are recurrent, or transient, periodic or aperiodic, and their periods. 7. For the Markov chains in the last problem, find their stationary distributions. 8. Let X1, be an i.i.d. sequence of random variables and let S" = 221:1 Xn. Is Xn = is” always convergent in probability, in mean square sense, in distribution and almost surely? If Xn has finite mean and variance, what can say about these questions? 9. The following are problems from your textbook. Some of the problems have been assigned as homework problems. 0 Section 4.1, problems 1, 0 Section 4.2, problems 2, 0 Section 4.3, problems 1, 0 Section 4.4, problems 1-6, 0 Section 4.5, problems 4,8, 0 Section 4.6, problems 4,6,7, 0 Section 4.7, problems 1,3,7,14, 0 Section 4.8, problems 1,3,4,5,6, h 5‘6? Mnsmon mx V“ e‘” V\ P: BLB-‘W A D «diagonalM/K u\ now (He mfhoak on M 22’ Infieurem 3. fig) : Z 31(3)“ h "‘1‘ '3 Pun '\’ 0“ M5)P\13. m1 :J“ 9, (“tel/(MK MWH’CHMW hm' (“5m | . how[fl¢_\_r_\_\i hmGS Vi“ W—l‘he ramde VlSH—- w hem I13 Mum‘bv- J_ fwfy.) ' ...
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