Interactive Distribution Visualizations

Explore and understand key probability distributions through interactive visualizations.

About This Tool

Understanding probability distributions is fundamental to data science and statistics. This interactive tool lets you visualize and manipulate different distributions to build intuition about their properties and use cases.

📊 Normal (Gaussian) Distribution

The bell curve - fundamental to statistics. Characterized by mean (μ) and standard deviation (σ).

0
1

Key Properties:

  • ~68% of data within 1σ of mean
  • ~95% of data within 2σ of mean
  • ~99.7% of data within 3σ of mean (Empirical Rule)
  • Use Cases: Heights, test scores, measurement errors, CLT applications

🎲 Binomial Distribution

Models the number of successes in n independent trials with probability p.

20
0.5

Key Properties:

  • Mean = n × p = 10
  • Variance = n × p × (1-p) = 5
  • Use Cases: Conversion rates, click-through rates, A/B test outcomes, quality control

⏱️ Poisson Distribution

Models the number of events in a fixed interval of time or space.

5 events per interval

Key Properties:

  • Mean = Variance = λ
  • Events occur independently
  • Average rate is constant
  • Use Cases: Page views per hour, customer arrivals, system failures, email volume

⏳ Exponential Distribution

Models the time between events in a Poisson process.

1 events per unit time

Key Properties:

  • Mean = 1/λ = 1.00
  • Memoryless property
  • Always right-skewed
  • Use Cases: Time until next customer, server response times, system lifetimes, wait times
15 mins Intermediate