Random Walks
Sequences of random steps.
Key idea
Sequences of random steps.
In depth
A random walk adds independent random steps. After n steps of ±1, the position has mean 0 and standard deviation √n. In 1D and 2D, it returns to the origin with probability 1; in 3D, not.
Worked example
A drunkard’s walk after 100 steps is typically about 10 units from the start.
Real-world uses
- Modelling stock price moves, animal movement and the spread of particles in physics
Common mistake
Expecting the walker to stay close to the origin.
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 Random Walks?
Sequences of random steps. It is a topic at the expert level in Probability & Statistics.
Where is Random Walks used in real life?
Real-world examples: Modelling stock price moves, animal movement and the spread of particles in physics.
What should I learn before Random Walks?
Make sure you are comfortable with Monte Carlo Simulation, the previous topic in Probability & Statistics.
What is a common mistake with Random Walks?
Expecting the walker to stay close to the origin.
How can I practise Random Walks?
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 Random Walks?
Move on to Markov Chains 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.