Question

Is there a unique way of filling in the missing probabilities in the transition diagram? If so, identify the missing probabilities. If not, explain why. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.

had to cut it into half split it's the top and bottom

Answer 1

We often list the transition probabilities in a matrix. The matrix is called the state transition matrix or transition probability matrix, P.

pij = Probability of transition from i toj Fram transition diagram PBA = 0.3 PAL 12 ? 0.3 PAB = 0.3 0-3 B 0.6 A w 072 PBB = 0:3 PCA = 0.7 pcc = 0.2 С O Probability transition matrix P:

B P = 4? 0.3 J=1 0.2 0.6 Also, E bij 1 B0.3 0.3 þBC co 7 PCB Hence for row 1: PAA + 0.3+0.6=1 => PAA = 0.1 Similarly, PBC + 8.3 +0.3=1 => PBC =0.4 PeB to 7+ 0.2=1 => PCB = 0.1 Hence, A is correct and prob- of transition from A to A is o.1, from B to c is 0.4 and from cto B is o.1