Natural Language Processing · M2 · mocks

Q2 (2 marks)

M2 Mock B · unseen pairs & decoding

M2 · confirmed 2 + 2 + any two of 3 + 3 + 3 · worked practice

Q2

A first-order Markov model starts in state A with probability 0.7. P(B|A)=0.4 and P(A|B)=0.3. Compute the path probability A→B→A, with no end-state factor. (2 marks)

Given

Start A=0.7; A→B=0.4; B→A=0.3.

To find

Probability of this state path.

Formula and why it applies

P(A,B,A)=P(A)P(B\mid A)P(A\mid B)

First-order dependence uses only the previous state for each transition.

Solution

Step 1. First transition contribution

0.7\times0.4=0.28

Step 2. Second transition contribution

0.28\times0.3=0.084

Path probability=0.084.