Hi i have an exercise and have a trouble with it if anyone can help me i would appreciate it plz help if you can.

This is the exercise:

Suppose the weather in a city in the (n) day is described from a Markov chain and it depend on the (n-1) day as follows:

1. if in (n-1) day rains then in (n) day rains with probability 60% or will be sunshine with probability 40%

2. if in (n-1) day has sunshine then in (n) day will have sunshine with probability 60% or will have clouds with probability 40%.

3. if in (n-1) day have clouds then in (n) day will rain with probability 20% , will have sunshine with probability 20% , will have clouds with probability 55% or will snow with probability 5%.

4. if in (n-1) day snows then in (n) day will have clouds with probability 90% or will snow with probability 10%

The exercise asks for the following:

1. Markov chain transition matrix

2. Solve the balanced equations and calculate the steady-state probabilities .

Thanks in advance