Markov Chains
Overview
Random Initial State
Suppose that the intial state {% x_0 %} is unknown, but known to have a given probability distribution. For example for a three state system,
the following vector might represent the probabilities of the system being in each state ({% x_0, x_1, x_2%})
{%
intial = \begin{bmatrix}
P_{0} \\
P_{1} \\
P_{2} \\
\end{bmatrix}
%}
Then the probability of
{% Probabilities = P^n \times inital %}
