Example 2.2

Consider you have an experiment which consists of trials each of which has three (3) outcomes, and the trials are dependent and we have the transition probability matrix as . Assume initial condition as ,  and , with the additional conditional that . Then find ,  and  in terms of the transition probability values,  and .

Example 2.3

Let us further extend example 2.5, where you have an experiment which consists of , trials. For the case

(i) , each of the trial has 5 outcomes, and the trials are not independent but have the transition probability matrix such that ,

(ii) when , each has 10 outcomes, and the trials are not independent but have the transition probability matrix such that ,

(iii) finally for the case , each has  outcomes, and the trials are not independent but have the transition probability matrix given by Poisson distribution, , with mean of 3 and remember that .

For the three different sub-problem let us consider the initial conditions as (i) , , (ii) ,  and (iii) Poisson distribution with mean of 3. With this set of information one can easily find (i) , for , , , (ii) , for, , , (iii) , for, , .