Higher Education · Probability & Statistics
Markov Chains
What is it
Undergraduate Markov chain study extends Further Maths work to formal proofs of long-run behaviour, including stationary distributions (the long-term probability of being in each state) and conditions for convergence.
Why it matters
Markov chains underlie some of the most important algorithms in modern computing — including the Markov Chain Monte Carlo methods used throughout Bayesian statistics and machine learning to sample from otherwise intractable probability distributions.
Exam tip
To find a stationary distribution, set up and solve πP = π (where P is the transition matrix) alongside the condition that probabilities sum to 1 — forgetting the summing-to-1 condition leaves the system with infinitely many solutions instead of one.
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