Question

Is there a unique way of filling in the missing probabilities in the transition​ diagram? If​ so, complete the transition diagram and write the corresponding transition matrix. If​ not, explain why.

A transition diagram has two states, A and B. An arrow pointing from A to A is labeled 0.5. An arrow pointing from A to B is labeled with a question mark. An arrow pointing from B to B is labeled with a question mark. An arrow pointing from B to A is labeled 0

Is there a unique way of filling in the missing probabilities in the transition​ diagram?

Answer 1

There are only two states A and B right?. Probability that an object in A to remain in A is 0.5. The only other option available for the object in state A is to go to B. Hence the probability for that is 1-0.5=0.5.

Now suppose the object is in B , There are again two options available. one is to remain in B or to move to A. Probability of moving to A from B is 1 (Sure event). That means it has 0 possibility to remain in B

This can be put together in a transition probability matrix as

ie A to A is 0.5

A to B is 0.5

B to A is 1 and B to B is 0