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# Markov chain calculator

If you want steady state calculator click here Steady state vector calculator. This calculator is for calculating the Nth step probability vector of the Markov chain stochastic matrix. This matrix describes the transitions of a Markov chain. This matric is also called as probability matrix, transition matrix, etc. A very detailed step by step solution is provided

Enter the Markov chain stochastic matrix Use ',' to separate between values. Use newline for new row: 0.5,0.5 0.8,0.2

## You can see a sample solution below. Enter your data to get the solution for your question

$$\displaylines{---}$$
$$\displaylines{ \mathbf{\color{Green}{Let's\;call\;all\;possible\;states\;as\;}} \begin{bmatrix} 1 & 2 & \end{bmatrix} \\ \\ \mathbf{\color{Green}{First\;we\;have\;to\;create\;Stochastic\;matrix}} \\ \\ Stochastic\;matrix\;=\;P= \begin{bmatrix} * & 1 & 2 & \\ \\ 1 & 0.5 & 0.5 & \\ \\ 2 & 0.8 & 0.2 & \end{bmatrix} \\ \\ Initial\;state\;=\;I\;= \begin{bmatrix} 0 & 1 & \end{bmatrix} \\ \\ \mathbf{\color{Green}{Probability\;of\;states\;after\;1st\;step\;=\;I*P\;=}} \\ \\ \begin{bmatrix} 0 & 1 & \end{bmatrix} * \begin{bmatrix} 0.5 & 0.5 & \\ \\ 0.8 & 0.2 & \end{bmatrix} \\ \\ \Rightarrow \begin{bmatrix} 0.8 & 0.2 & \end{bmatrix} \\ \\ \mathbf{\color{Green}{In\;same\;way}} \\ \\ I*P^{ 2 }=I*P^{ 1 }*P= \\ \\ \Rightarrow \begin{bmatrix} 0.8 & 0.2 & \end{bmatrix} * \begin{bmatrix} 0.5 & 0.5 & \\ \\ 0.8 & 0.2 & \end{bmatrix} \\ \\ \Rightarrow \begin{bmatrix} 0.56 & 0.44 & \end{bmatrix} \\ \\ I*P^{ 3 }=I*P^{ 2 }*P= \\ \\ \Rightarrow \begin{bmatrix} 0.56 & 0.44 & \end{bmatrix} * \begin{bmatrix} 0.5 & 0.5 & \\ \\ 0.8 & 0.2 & \end{bmatrix} \\ \\ \Rightarrow \begin{bmatrix} 0.632 & 0.368 & \end{bmatrix} \\ \\ I*P^{ 4 }=I*P^{ 3 }*P= \\ \\ \Rightarrow \begin{bmatrix} 0.632 & 0.368 & \end{bmatrix} * \begin{bmatrix} 0.5 & 0.5 & \\ \\ 0.8 & 0.2 & \end{bmatrix} \\ \\ \Rightarrow \begin{bmatrix} 0.6104 & 0.3896 & \end{bmatrix} \\ \\ \mathbf{\color{Green}{Probability\;after\;4\;step\;is\;}} \begin{bmatrix} 0.6104 & 0.3896 & \end{bmatrix} }$$