Study Guide

Learning Objectives

• Construct two-state transition matrix models (4.14.A.1).
• Predict future states with T v and n-step products (4.14.B.1).
• Identify steady state via repeated multiplication (4.14.B.2).
• Predict past states with inverse when defined (4.14.B.3).
• Construct models and support conclusions (1.C, 3.B, 3.C).

Course scope only (Unit 4 additional topic; not on the AP Exam).

Suggested Practice Sequence

1. Read transition percents from a story. 2. Build T and initial state vector v. 3. Compute one-step and n-step predictions. 4. Explore steady state with repeated multiply. 5. Justify predictions with context and data.

Classroom / Check-In Moves

• What does entry T_ij mean in words?
• Does the predicted distribution match the story?
• Is this steady state unchanged by T?

Misconception Watch-List

• Swapping row/column state meaning.
• Forgetting self-transition (stay) rates.
• Treating steady state as always 50-50.

Vocabulary to Own

• transition matrix; state vector
• discrete interval; steady state
• future state; past state

Materials Map

• Practice: build model, predict, steady state
• Word: contextual transition stories
• Mixed / multi-*: combine with 4.10-4.13
• Review and practice test: modeling fluency
• Interactive: transition and steady-state checks