Intelligent Systems II · TEE · papers

Q1(d) Savings and current accounts (Markov chain) [5]

Re-examination · 31 Jan 2026

Actual TEE re-exam · 100 marks · 3 hours · Q1 compulsory + any 4 of Q2–Q7 · every answer verified (key errors flagged)

Question. Each year 20% of Savings holders switch to Current and 80% stay; 10% of Current holders switch to Savings and 90% stay. (a) Construct the transition matrix. (b) Draw the state diagram. [5 marks]

Answer

Given

All transition values are given in the full question. State order: S, C.

To find

The transition matrix and state diagram.

Formula and why it applies

Rows mean current state; columns mean next state. For each destination, multiply each origin amount by its transition probability, then add.

Solution

Step 1. Convert every origin row to probabilities
From / ToSC
S0.80.2
C0.10.9

Each row sums to 1 because it lists all possible destinations for that origin. A percentage is divided by 100: 25%=.25.

Step 2. Interpret entries and draw the transitions

Diagonal entries are the fractions staying at their current state; off-diagonal entries are fractions moving to a different state. Each arrow uses its origin row and destination column. These fractions have different origin populations, so adding raw column probabilities does not give the number arriving.

Swipe across the diagram to read its labels ↔
Each arrow is labelled with the probability of that transition.
Diagram: Each arrow is labelled with the probability of that transition.. Labels: Savings (S) and Current (C) accounts per year | 0.2 | 0.1 | 0.8 | 0.9 | S | C
Each arrow is labelled with the probability of that transition.
Final answer. The transition matrix and state diagram are given above.