This note is purely in English for my final exam, please be calm down if you are in trouble.
Lets use Markov Chain to solve a very simple problem - 'Weather Problem', we have the following assumptions:
- If it is raining today, then the probability of raining tomorrow is 70%, and the probability of not raining tomorrow is 30% ;
- If it is not raining today, then the probability of raining tomorrow is 40%, and the probability of not raining tomorrow is 60% .
Therefore, we have the following finite state machine:
According to the state machine, we can get the one-step transition matrix as follows:
Now, lets use the stationary probability of Markov Chain, for computing the statistical probability of raining or not raining for someday.
- At first, we make the staring distribution in Day 0 is
- Then, the distribution in Day 1 is
- Then, the distribution in Day 2 is
- Finally, for given transition matrix and the staring distribution, the stationary distribution can be computed as
Actually, we have already got our goal, the final stationary distribution can describe the statistical probability.
In conclusion, just need 3 steps for analysis of practical example using Markov Chain.
- Draw the State Machine through the existing conditions;
- Compute the one-step transition matrix;
- Compute the stationary distribution according to the existing conditions.
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