Setting Up and Interpreting Transition Matrices (VCE SSCE General Mathematics): Quizzes

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Setting Up and Interpreting Transition Matrices
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What does a transition matrix describe?

How things move between states over time

In a transition matrix, what do the columns represent?

The starting state

In a transition matrix, what do the rows represent?

The ending state

In a transition matrix, what must each column sum to?

11 (or 100%100\%)

How many states require a 3×33 \times 3 transition matrix?

Three states

If 0.850.85 of operating machines stay operating, what proportion break down?

0.150.15

If 5050 cars rent in Bendigo & 0.80.8 return there, how many return to Bendigo?

4040 cars

What proportion equals 25%25\%?

0.250.25

If 77%77\% stay in Benalla, what % are not expected to return to Benalla?

23%23\%

Which matrix follows transition rules? (columns must sum to 11)

[0.70.20.30.8]\begin{bmatrix}0.7&0.2\\0.3&0.8\end{bmatrix}

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