Bernoulli Distribution
A single yes/no trial.
Key idea
A single yes/no trial.
In depth
One trial with two outcomes: success with probability p, failure with 1 − p. Mean p, variance p(1 − p). It is the building block of the binomial and geometric distributions.
Worked example
A free throw with 80% success: X = 1 with probability 0.8, mean 0.8, variance 0.16.
Formula
Real-world uses
- Modelling a single yes/no event such as a customer buying a product or a light bulb working
Common mistake
Using it for trials with more than two outcomes.
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 Bernoulli Distribution?
A single yes/no trial. It is a topic at the advanced level in Probability & Statistics.
What is the formula for Bernoulli Distribution?
The key formula is P(1) = p.
Where is Bernoulli Distribution used in real life?
Real-world examples: Modelling a single yes/no event such as a customer buying a product or a light bulb working.
What should I learn before Bernoulli Distribution?
Make sure you are comfortable with Linearity of Expectation, the previous topic in Probability & Statistics.
What is a common mistake with Bernoulli Distribution?
Using it for trials with more than two outcomes.
How can I practise Bernoulli 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 Bernoulli Distribution?
Move on to Binomial Distribution next.
Related advanced topics in Probability & Statistics
- Quartiles and IQR – Quartiles split data into four parts; IQR = Q3 − Q1.
- Box Plots – Five-number summary visualised.
- Outliers – Values beyond 1.5 IQR from the quartiles.
- Variance – Average squared deviation from the mean.
- Standard Deviation – Square root of variance; typical spread.
- Sample vs Population Variance – Divide by n−1 for sample variance.