In class we are working on DTMCs for past couple of week, and in our last lecture we did an example. Question was:
In a city of nowhere it only rains if there are clouds for successive m-days. Any given day is cloudy with probability 'p', and it is independent of all previous days. What is the expected number of days before it rains.
One simplest of models is to consider number of days as States, that is let Day 0 be state 1, Day 1 be state 2, .... , Day m be the state m. Each state goes up one state with probability p and goes down to the first state with probability 1-p. This model will give us the stationary probability of state i, that can later be used to calculate the Expected Value.
I was wondering if there is any simpler model than this one? Any Ideas?
Regards,