Markov Chains
Processes where the future depends only on the present.
Key idea
Processes where the future depends only on the present.
In depth
A Markov chain has the property that the next state depends only on the current state. A transition matrix gives probabilities, and many chains converge to a steady-state distribution.
Worked example
Weather: sunny → sunny 0.8, rainy → rainy 0.6; long-run rainy fraction = 0.2/(0.2 + 0.4) = 1/3.
Real-world uses
- Predicting weather patterns, website navigation and customer switching between products
Common mistake
Assuming history matters when the Markov property holds, or vice versa.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Markov Chains?
Processes where the future depends only on the present. It is a topic at the expert level in Probability & Statistics.
Where is Markov Chains used in real life?
Real-world examples: Predicting weather patterns, website navigation and customer switching between products.
What should I learn before Markov Chains?
Make sure you are comfortable with Random Walks, the previous topic in Probability & Statistics.
What is a common mistake with Markov Chains?
Assuming history matters when the Markov property holds, or vice versa.
How can I practise Markov Chains?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Markov Chains?
Move on to Poisson Process next.
Related expert topics in Probability & Statistics
- Skewness and Kurtosis – Measures of asymmetry and tail heaviness.
- Residuals and R² – Error of a fit and proportion of variance explained.
- Simpson’s Paradox – A trend reverses when groups are combined.
- Law of Total Probability – Split an event over a partition.
- Bayes’ Theorem – Update beliefs with evidence.
- Medical Tests and Base Rates – Why positive results can still be probably false.