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What does entry (row i, column j) of a transition matrix mean?
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All Flashcards in Topic 4.19
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4.19.18 cards
What does entry (row i, column j) of a transition matrix mean?
The probability of moving FROM state j INTO state i in one step.
Why do the columns of a transition matrix sum to 1?
Everyone who starts in that state (column) must end up in some state, so the probabilities over all destinations total 1.
How do you step a Markov chain forward one period?
Multiply the transition matrix by the current state vector: s₁ = T s₀.
State vector after n steps?
sₙ = Tⁿ s₀ — raise T to the power n, then multiply by the start vector.
How do you turn '70% of A return to A, 30% switch to B' into a matrix?
Column A is 0.7 in the A-row and 0.3 in the B-row (column = where you start, row = where you end).
On the GDC, how do you get the population after n weeks?
Store T and s₀, then compute T^n and the product T^n × s₀.
Is a transition matrix usually symmetric?
No — the chance of A→B need not equal B→A, so it is generally not symmetric.
After computing sₙ, what extra step earns marks in AI HL?
Interpret the numbers IN CONTEXT — say which group/café/patch they describe and round sensibly.
Topic 4.19 study notes
Full notes & explanations for Markov chains (HL only)
Math AI exam skills
Paper structures, command terms & tips
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