3. The transition matrix for a three-state Markov chain is 0 ||1 0 r llo q p+r Р P = q Where p, q> 0, r≥ 0 and p + q + r = 1 a. Draw the directed graph of the chain. b. Is the set {2,3} closed? Why or why not? c. Find the expression for Pn). Then verify that state 1 is positive recurrent. d. Show that the process has a unique stationary probability distribution = (1₁, 1₂, 13) tr

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3. The transition matrix for a three-state Markov chain is
E
10 0
9 r
lo q p+1
P =
J
Where p, q > 0, r ≥ 0 and p + q + r = 1
a. Draw the directed graph of the chain.
b. Is the set {2,3} closed? Why or why not?
c. Find the expression for P). Then verify that state 1 is positive recurrent.
d. Show that the process has a unique stationary probability distribution =
(1₁, 1₂, 13).
Transcribed Image Text:3. The transition matrix for a three-state Markov chain is E 10 0 9 r lo q p+1 P = J Where p, q > 0, r ≥ 0 and p + q + r = 1 a. Draw the directed graph of the chain. b. Is the set {2,3} closed? Why or why not? c. Find the expression for P). Then verify that state 1 is positive recurrent. d. Show that the process has a unique stationary probability distribution = (1₁, 1₂, 13).
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