Probability Distributions
Assign probabilities to values of a random variable.
Key idea
Assign probabilities to values of a random variable.
In depth
A distribution lists the values a random variable can take with their probabilities (or a density for continuous ones). Probabilities must be non-negative and sum (or integrate) to 1.
Worked example
Number of heads in 2 flips: P(0) = 1/4, P(1) = 1/2, P(2) = 1/4.
Real-world uses
- Describing how many goals a football team might score
- Predicting game-day sales
Common mistake
Probabilities that do not total 1.
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 Probability Distributions?
Assign probabilities to values of a random variable. It is a topic at the advanced level in Probability & Statistics.
Where is Probability Distributions used in real life?
Real-world examples: Describing how many goals a football team might score; Predicting game-day sales.
What should I learn before Probability Distributions?
Make sure you are comfortable with Random Variables, the previous topic in Probability & Statistics.
What is a common mistake with Probability Distributions?
Probabilities that do not total 1.
How can I practise Probability Distributions?
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 Probability Distributions?
Move on to Expected Value 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.