Hi.. I need the SOLUTION of PART (2) for SURE! Exercise instructions (1) The sim

Question

Hi.. I need the SOLUTION of PART (2) for SURE!

Exercise instructions

(1) The simple Markov chain model of the weather had only two states "Sunny" and "Rainy"; add a third state "Cloudy". The transition probabilites are: Sunny > Sunny 0.7, Sunny > Rainy 0.2, Sunny > Cloudy 0.1; Rainy > Sunny 0.4, Rainy > Rainy 0.4, Rainy > Cloudy 0.2; Cloudy > Sunny 0.3, Cloudy > Rainy 0.3, Cloudy > Cloudy 0.4. Implement the transition matrix for this three-state weather model.

(2) Use the three-state weather model and matrix multiplication to calculate the probabilies for each state on days 2 - 5. Assume that the weather is Sunny on day 1.

Thnx for the help!!!!!!

Explanation / Answer

Ans:

1)Transition probability matrix P=

2)Intial distribution=[1 0 0]

First find out 2 -step trsnsition matrix,P2:

distribution at day 2=[0.6 0.25 0.15]

Now,calculate 5-step transition matrix,P5:

distribution at day 5=[0.547 0.272 0.181]

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