Exponential Distribution
Waiting times between events.
Key idea
Waiting times between events.
In depth
Models waiting time between Poisson events with rate λ: density λe^(−λx), mean 1/λ. It is memoryless: P(X > s + t | X > s) = P(X > t).
Worked example
Buses arrive at rate 2 per hour: P(wait > 30 min) = e^(−1) ≈ 0.368.
Formula
Real-world uses
- Modelling the time between customer arrivals or the lifetime of a light bulb
Common mistake
Confusing the rate λ with the mean 1/λ.
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 Exponential Distribution?
Waiting times between events. It is a topic at the expert level in Probability & Statistics.
What is the formula for Exponential Distribution?
The key formula is f(x) = λe^(−λx).
Where is Exponential Distribution used in real life?
Real-world examples: Modelling the time between customer arrivals or the lifetime of a light bulb.
What should I learn before Exponential Distribution?
Make sure you are comfortable with Standard Normal and z-Tables, the previous topic in Probability & Statistics.
What is a common mistake with Exponential Distribution?
Confusing the rate λ with the mean 1/λ.
How can I practise Exponential 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 Exponential Distribution?
Move on to Continuous Random Variables 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.