T company computer department purchases a new computer every two years with preferences for three models; T1, T2 and T3. If the present model is T1, the next computer may be T2 with probability 0.2 or T3 with probability 0.15. If the present model is T2, the probabilities of switching to T1 and T3 are 0.6 and 0.25 respectively. And if present model is T3 then, the probabilities of switching to T1 and T2 are 0.5 and 0.1 respectively. Represent the situation as a Markov chain
T company computer department purchases a new computer every two years with preferences for three models; T1, T2 and T3. If the present model is T1, the next computer may be T2 with probability 0.2 or T3 with probability 0.15. If the present model is T2, the probabilities of switching to T1 and T3 are 0.6 and 0.25 respectively. And if present model is T3 then, the probabilities of switching to T1 and T2 are 0.5 and 0.1 respectively.
Represent the situation as a Markov chain
Let be preference of a computer for every two years.
A stochastic process with state space
where are three computers models the transition probability matrix is given by
is the conditional probability of transition from state at trial to the state at trail.
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