Assignment – Module 5
1. Daily weather at a place may be considered as a two state Markov Chain, with the
transition probability matrix (TPM) given by
W D
W 0.7 0.3
D 0.4 0.6
where W indicates a rainy day and D a dry day. What is the probability that it will be a
rainy day four days from today, given that today is a rainy day? Obtain the steady state
probability of a rainy day.
2. Consider a 2-state, first order homogeneous Markov Chain for a sequence of wet and dry
days. State 1 is dry and state 2 is wet. The transition probability matrix for the Markov
Chain is given by
dry wet
dry 0.8 0.2
wet 0.4 0.6
What is the probability of the day 3 being in wet state, if day 0 is a dry day?
3. Consider a Markov chain model for daily rainfall in a subcatchment. Consider state-1
represents a dry condition, state-2 represents an intermediate rainfall condition and state-
3 represents a completely saturated condition. Assume the transition probability matrix is
0.1 0.4 0.5
0.1 0.7 0.2
0.1 0.6 0.3
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