Poisson Process
Random events at constant average rate.
Key idea
Random events at constant average rate.
In depth
Events occur randomly in continuous time at an average rate λ, with independent counts in disjoint intervals. Counts are Poisson(λt) and waiting times are exponential(λ).
Worked example
Emails at 6 per hour: expected 3 in 30 minutes.
Real-world uses
- Modelling arrivals at a shop, emails received per hour and earthquakes over time
Common mistake
Using it when events are bursty or have a daily pattern.
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 Poisson Process?
Random events at constant average rate. It is a topic at the expert level in Probability & Statistics.
Where is Poisson Process used in real life?
Real-world examples: Modelling arrivals at a shop, emails received per hour and earthquakes over time.
What should I learn before Poisson Process?
Make sure you are comfortable with Markov Chains, the previous topic in Probability & Statistics.
What is a common mistake with Poisson Process?
Using it when events are bursty or have a daily pattern.
How can I practise Poisson Process?
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 Poisson Process?
Move on to Time Series Basics 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.