Answer:
The Question is incomplete. Here is the complete Question:
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
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.
Explanation: