MARKOV CHAINS and transition probabilities

Hi,

Can anyone help with this problem. I am trying to write down the matrix of transition probabilities for this scenario below.

Suppose every Friday Dave takes his wife out to eat. They always eat at KFC, Pizzahut, Nandos or Chiquitos. after visiting KFC they always go to Pizzahut the following Friday. Also if they visited Pizzahut one Friday the visit KFC or Chiquitos the next and they are twice as likely to visit Chiquitos than KFC. After visiting NAndos they are equally likely to go to any of the three restaurants, similarly after visiting Chiquitos the are equally likely to go to any of the othe four the next Friday.

I have written this matrix as

1/2 1/2 0 0
1/3 0 0 2/3
1/3 1/3 0 0
1/4 1/4 1/4 1/4

Not so sure if this is correct. Any help would be appreciated. Thanks

Hello, Sashoye!

Suppose every Friday Dave takes his wife out to eat.
They always eat at KFC, Pizzahut, Nandos or Chiquitos.
After visiting KFC, they always go to Pizzahut the following Friday.
If they visited Pizzahut one Friday, they visit KFC or Chiquitos the next,
and they are twice as likely to visit Chiquitos than KFC.
After visiting Nandos, they are equally likely to go to any of the other three restaurants.
Similarly after visiting Chiquitos, they are equally likely to go to any of the four the next Friday.

Click to expand...

\(\displaystyle \quad \begin{array}{c|c|c|c|c|}
& KFC & PH & Na & Ch \\ \hline
KFC & 0& 1 & 0&0 \\ \hline
PH & \frac{1}{3} &0&0&\frac{2}{3} \\ \hline
Na & \frac{1}{3} & \frac{1}{3} & 0 & \frac{1}{3} \\ \hline
Ch &\frac{1}{4} & \frac{1}{4} & \frac{1}{4} & \frac{1}{4} \\ \hline
\end{array}\)

soroban said:

Hello, Sashoye!



\(\displaystyle \quad \begin{array}{c|c|c|c|c|}
& KFC & PH & Na & Ch \\ \hline
KFC & 0& 1 & 0&0 \\ \hline
PH & \frac{1}{3} &0&0&\frac{2}{3} \\ \hline
Na & \frac{1}{3} & \frac{1}{3} & 0 & \frac{1}{3} \\ \hline
Ch &\frac{1}{4} & \frac{1}{4} & \frac{1}{4} & \frac{1}{4} \\ \hline
\end{array}\)

Click to expand...

Thank you so much for your help!