Poisson Distribution
Counts of rare events in an interval.
Key idea
Counts of rare events in an interval.
In depth
Counts events in a fixed interval when events occur independently at a constant average rate λ: P(X = k) = e^(−λ)λᵏ/k!. Mean and variance are both λ. It approximates the binomial for large n and small p.
Worked example
A call centre averages 3 calls per minute: P(0 calls) = e⁻³ ≈ 0.05.
Formula
Real-world uses
- Predicting the number of calls a helpline gets per hour or accidents at a junction in a year
Common mistake
Using it when events cluster or the rate changes.
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 Distribution?
Counts of rare events in an interval. It is a topic at the expert level in Probability & Statistics.
What is the formula for Poisson Distribution?
The key formula is P(k) = λᵏe⁻λ/k!.
Where is Poisson Distribution used in real life?
Real-world examples: Predicting the number of calls a helpline gets per hour or accidents at a junction in a year.
What should I learn before Poisson Distribution?
Make sure you are comfortable with Geometric Distribution, the previous topic in Probability & Statistics.
What is a common mistake with Poisson Distribution?
Using it when events cluster or the rate changes.
How can I practise Poisson Distribution?
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 Distribution?
Move on to Hypergeometric Distribution 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.