For Exercise 9.3.1, Use R to simulate a Markov Chain and estimate the probabilit

Question

For Exercise 9.3.1, Use R to simulate a Markov Chain and estimate the probabilities in part (a) and part (b)

ar 4 derive the original Markov chain, P sencin 9.3.3 The following matrix is the single-step transition probability matrix of a chuir which describes the weather State 1 represents a sunny day, state 2 a cloudy day, and state 3 a rainy day Sunny Cloudy Rainy Sunny 0.7 0.2 0.1 P=Cloudy 0.3 0.5 0.2 Rainy 0.2 0.6 0.2 a) What is the probabaility of a sunny day being followed by two cloudy days? b Gve tut today is rainy, what is the probability that the su n will shine the day after tomorrow? mran Irngth of a rainy period?

Explanation / Answer

a) Probability of a sunny day being followed by two cloudy days is computed as:

S --> C --> C, Prob = 0.2*0.5 = 0.1

Therefore 0.1 is the required probability here.

b) Given that it is rainy today, the sun will shine a day after tomorrow here is computed as:

Therefore the total probability here is 0.04 + 0.18 + 0.14 = 0.36

Therefore 0.36 is the required probability here.

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