This student never eats the same kind of food for 2 consecutive weeks. If she eats a Chinese restaurant one week, then she is three times as likely to have Greek as Italian food the next week. If she eats a Greek restaurant one week, then she is four times as likely to have Chinese as Italian food the next week. If she eats a Italian restaurant one week, then she is five times as likely to have Chinese as Greek food the next week.

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This student never eats the same kind of food for 2 consecutive weeks. If she eats a Chinese restaurant one week, then she is three times as likely to have Greek as Italian food the next week. If she eats a Greek restaurant one week, then she is equally likely to have Chinese as Italian food the next week. If she eats a Italian restaurant one week, then she is four times as likely to have Chinese as Greek food the next week.

Assume that state 1 is Chinese and that state 2 is Greek, and state 3 is Italian.

Find the transition matrix for this Markov process. P=[]

Answer:

C G I

C 0 3/4 1/4

G 1/2 0 1/2

I 4/5 1/5 0

Step-by-step explanation:

In Markov chain/matrix, it is important to understand that it deals with the probability of the event in future given the present condition.

Let's say C = chinese, G = Greek, I = Italian.

The row of the transition matrix will represent FIRST WEEK, and the column will represent NEXT WEEK (future)

To make this simple and understandable, we build the matrix as shown below:

C G I

C C-C C-G C-I

G G-C G-G G-I

I I-C I-G I-I

note that C-C represent eating Chinese in one week, and also chinese in the next week, C-G represent eating Chinese in one week, and Greek in the next week, and so on ...

- 'This student never eats the same kind of food for 2 consecutive weeks' tells us the node of C-C, G-G, I-I will be zero

- 'If she eats a Chinese restaurant one week, then she is three times as likely to have Greek as Italian food the next week' means C-G = 3/4 and C-I = 1/4. You should have understand this since C-C = 0 and total probability of each row is equal to 1.

- Similarly, the sentence 'If she eats a Greek restaurant one week, then she is equally likely to have Chinese as Italian food the next week' gives us G-C = 1/2 and G-I = 1/2

- Lastly 'If she eats a Italian restaurant one week, then she is four times as likely to have Chinese as Greek food the next week' tells us I-C = 4/5 and I-G = 1/5

From these we construct the transition matrix based on the data given to us as follows:

C G I

C 0 3/4 1/4

G 1/2 0 1/2

I 4/5 1/5 0

To confirm our answer, each row must have total probability of 1.