Practice Flashcards
Flip to reveal answersWhat does entry (row i, column j) of a transition matrix mean?
Track your progress — Sign up free to save your progress and get smart review reminders based on spaced repetition.
All 8 Flashcards — Transition matrices
Sign up free to track progress and get spaced-repetition review schedules.
Question
What does entry (row i, column j) of a transition matrix mean?
Answer
The probability of moving FROM state j INTO state i in one step.
Question
Why do the columns of a transition matrix sum to 1?
Answer
Everyone who starts in that state (column) must end up in some state, so the probabilities over all destinations total 1.
Question
How do you step a Markov chain forward one period?
Answer
Multiply the transition matrix by the current state vector: s₁ = T s₀.
Question
State vector after n steps?
Answer
sₙ = Tⁿ s₀ — raise T to the power n, then multiply by the start vector.
Question
How do you turn '70% of A return to A, 30% switch to B' into a matrix?
Answer
Column A is 0.7 in the A-row and 0.3 in the B-row (column = where you start, row = where you end).
Question
On the GDC, how do you get the population after n weeks?
Answer
Store T and s₀, then compute T^n and the product T^n × s₀.
Question
Is a transition matrix usually symmetric?
Answer
No — the chance of A→B need not equal B→A, so it is generally not symmetric.
Question
After computing sₙ, what extra step earns marks in AI HL?
Answer
Interpret the numbers IN CONTEXT — say which group/café/patch they describe and round sensibly.
Read the notes
Full study notes for Transition matrices
Topic 4.19 hub
Markov chains (HL only)
More from Topic 4.19
All flashcards in this topic
Math AI exam skills
Paper structures & tips
Track your progress with spaced repetition
Sign up free — Aimnova tells you exactly which cards to review and when, so you remember everything before your IB exam.
Start Free