# Problem 1072

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

Solution:-

There are several conditions that must be satisfied in a transition diagram.

1)   The number on each arrow is a probability, it must be between 0 and 1.

2)   All the probability on the arrows from a state must sum to 1.

3)   For each state, if there is only one arrow from that state with missing probability, and if the known transition probability form that sum to 1 or less, then the missing value can be determined.

Consider state A.

The probability of transition from A to B is known

The probability of transition from A to C is known.

The probability of transition from A to A is computed as 1 – 0.25 = 0.6.

Consider state B.

The probability of transition from B to A is known.

The probability of transition from B to B is known.

The probability of transition from B to C is computed as 1 – 0.05 – 0.34 = 0.6.

Consider state C.

The probability of transition from C to A is known.

The probability of transition from C to C is known.

The probability of transition from C to B is computed as 1 – 0.45 – 0.45 = 0.1.

The corresponding transition matrix is

P =