7.6-07 Stationary distributions

Stationary distributions

Solve for stationary distributions by combining the fixed-vector equation with probability constraints. Compare unique, nonunique and periodic examples and derive a general two-state balance formula.

What you will practise

• Solve stationary equations
• Normalize by total mass
• Check nonnegativity and uniqueness
• Separate stationary states from convergence

Prerequisites and study approach

This microlearning belongs to Module 7, Eigenvalues and Dynamical Systems, in the Complete Linear Algebra Course. Before starting, review column-stochastic matrices, null spaces and linear systems. The questions move from recognition and short calculations to connected reasoning. Single-select questions require one answer; multiselect questions ask you to evaluate every statement independently.

The later problems examine convex mixtures, repeated transition columns and a parameterized two-state chain. Work out your own result before checking the choices, then use the explanation to compare the reasoning and diagnose a mistaken assumption. This focused practice connects conceptual understanding with reliable problem solving and supports review before the next microlearning.