STAT 333 tutorial8sol

# STAT 333 tutorial8sol - Stat 333 Tutorial 8...

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Stat 333 - Tutorial 8 Answers/Solutions 1. (a) 0.6665 (b) 0.6667 2. (a) Single Closed Class: { 0 , 1 , 2 } . All states are positive recurrent since we have a ﬁnite state space. (b) Single Closed Class: { 0 , 1 , 2 , 3 } . . One can note also that the states are periodic with d = 3 . (c) Classes: { 0 , 2 } (closed) and { 3 , 4 } (closed) and { 1 } (open). States 0, 2, 3, 4 are positive recurrent since we have a ﬁnite state spaces. State 1 is transient since it is an open class. (d) Classes: { 0 , 1 } (closed) and { 2 } (closed), { 3 } (open) and { 4 } (open). States 0, 1 and 2 are positive recurrent since we have a ﬁnite state spaces. States 3 and 4 is transient since they belong to open classes. 3. Deﬁne 0 := TT , 1 := HH , 2 := HT and 3 := TH . (a) i. P = 1-p 0 0 0 0 p 1-p 0 1-p 0 0 0 0 p 1-p 0 ii. Aperiodic, Positive Recurrent (and therefore Ergodic), and Irreducible. iii. As mentioned in class, you need to ﬁnd such that · P = with 3 j =0 π j = 1 . You can do this either the regular way or by means of row reduction on

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STAT 333 tutorial8sol - Stat 333 Tutorial 8...

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