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I have a simple markov chain with A, B and C states. For each state I have a probability and beyond that, a value. So, for each state transition I have two informations: the probability of the transisiton to another state and a value.

I need to know the average value considering that I am trying to start from node A and finish in the node C. I was thinking about to use Markov Chains but I have a value with the probability and I dont know whet kind of theory I can apply to find the average value on this path A -> C.

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Writing $e_A$ for the value of $A$ and $e_B$ for the value of $B,$ your diagram indicates

$$\begin{aligned} e_A &= 0.05(5+e_A) + 0.90(2+e_B) + 0.05(10)\\ e_B &= 0.50(3+e_A) + 0.50(3+e_B). \end{aligned}$$

Solve these simultaneous linear equations for $e_A$ and $e_B.$

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  • $\begingroup$ Ok, then what I need to do after finding the two variables? $\endgroup$
    – Caio Correia
    Commented Dec 27, 2020 at 21:51
  • $\begingroup$ $e_A$ is the answer to your question. $\endgroup$
    – whuber ♦
    Commented Dec 28, 2020 at 13:25

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