A Dinner Club goes out to eat once a week. It visits three kinds of restaurants, Asian, Mediterranean, and Mexican, but they never visit the same type of restaurant two weeks in a row. If they go to an Asian restaurant one week then they are equally likely to go to a Mediterranean as a Mexican the next week. If they go to a Mediterranean restaurant one week then they are two times as likely to to go to an Asian as a Mexican the next week. If they go to a Mexican restaurant one week then they are three times as likely to go to an Asian as a Mediterranean the next week. If we think of this as a Markov Chain in which state 1 is Asian, state 2 is Mediterranean, and state 3 is Mexican, then what is the transition matrix? 1 2 ½ (B) (A) (C) (D) 17 1/ 3 31 1/ 1/ 21 1/

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A Dinner Club goes out to eat once a week. It visits three kinds of restaurants, Asian,
Mediterranean, and Mexican, but they never visit the same type of restaurant two
weeks in a row. If they go to an Asian restaurant one week then they are equally likely
to go to a Mediterranean as a Mexican the next week. If they go to a Mediterranean
restaurant one week then they are two times as likely to to go to an Asian as a Mexican
the next week. If they go to a Mexican restaurant one week then they are three times
as likely to go to an Asian as a Mediterranean the next week. If we think of this as
a Markov Chain in which state 1 is Asian, state 2 is Mediterranean, and state 3 is
Mexican, then what is the transition matrix?
w - - -
/2 ½
(A)
(B)
2 1
2/3
(C)
1/2
(D)
1/2
1 %
1½½ 0
1/3
1
1 2 2
(E)
2/2 0 3
(F)
22 1 ½
/3
(G)
1/2
(H)
A
O D
O E
OF
G
Transcribed Image Text:A Dinner Club goes out to eat once a week. It visits three kinds of restaurants, Asian, Mediterranean, and Mexican, but they never visit the same type of restaurant two weeks in a row. If they go to an Asian restaurant one week then they are equally likely to go to a Mediterranean as a Mexican the next week. If they go to a Mediterranean restaurant one week then they are two times as likely to to go to an Asian as a Mexican the next week. If they go to a Mexican restaurant one week then they are three times as likely to go to an Asian as a Mediterranean the next week. If we think of this as a Markov Chain in which state 1 is Asian, state 2 is Mediterranean, and state 3 is Mexican, then what is the transition matrix? w - - - /2 ½ (A) (B) 2 1 2/3 (C) 1/2 (D) 1/2 1 % 1½½ 0 1/3 1 1 2 2 (E) 2/2 0 3 (F) 22 1 ½ /3 (G) 1/2 (H) A O D O E OF G
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