Transition Matrix Example

Example: Transition Matrix

Consider state space whether it rains today (state 0) or will be sunny (state 1).

Let the transition probabilities:

• $P_{00}=\alpha$: Probability it rains (0) today, then stay in rains (0) tomorrow
• $P_{10}=\beta$: Probability it’s sunny (1) today, then change to rains (0) tomorrow

The transition matrix is:

$\mathbf{P}=\Vert \begin{array}{cc}\alpha & 1-\alpha \\ \beta & 1-\beta \end{array}\Vert$

Where:

• $P_{01}=1-\alpha$: Probability it rains (0) today, then change to sunny (1) tomorrow
• $P_{11}=1-\beta$: Probability it’s sunny (1) today, then stay sunny tomorrow

Related

• Transition Probability Matrix
• n-step Transition Matrix Example