Common Probability Distributions
February 22, 2026Common Probability Distributions #
Once you can describe a random variable using a pmf or pdf, the next step is to use named distributions that appear repeatedly in real data and in ML models.
Key takeaway: Named distributions give you ready-made probability models for common patterns: binary outcomes, counts, and measurement noise.
flowchart TD PD["Probability<br/>distributions"] --> DS["Common<br/>distributions"] DS --> DIS["Discrete"] DS --> CON["Continuous"] DIS --> D1["Bernoulli"] DIS --> D2["Binomial"] DIS --> D3["Poisson"] CON --> D4["Normal<br/>(Gaussian)"] CON --> D5["t / Chi-square / F<br/>(intro)"] style PD fill:#90CAF9,stroke:#1E88E5,color:#000 style DS fill:#90CAF9,stroke:#1E88E5,color:#000 style DIS fill:#CE93D8,stroke:#8E24AA,color:#000 style CON fill:#CE93D8,stroke:#8E24AA,color:#000 style D1 fill:#C8E6C9,stroke:#2E7D32,color:#000 style D2 fill:#C8E6C9,stroke:#2E7D32,color:#000 style D3 fill:#C8E6C9,stroke:#2E7D32,color:#000 style D4 fill:#C8E6C9,stroke:#2E7D32,color:#000 style D5 fill:#C8E6C9,stroke:#2E7D32,color:#000
1) Bernoulli distribution (binary) #
Use when: one trial has two outcomes (success/failure).