Maths Learning

Probability Distribution - Function, Formula, Table

Understanding probability distributions, their functions, formulas, and tables

Interactive Probability Distribution Visualization

Welcome to the Probability Distribution Explorer

This interactive visualization helps you understand different probability distributions, their properties, and how parameters affect their shape. Explore discrete and continuous distributions with real-time parameter adjustments.

What you can explore:

  • Discrete Distributions: Binomial, Poisson, Geometric (PMF)
  • Continuous Distributions: Normal, Uniform, Exponential (PDF)
  • Properties: Mean, variance, standard deviation
  • Cumulative Distribution: CDF visualization

How to Use This Visualization

Interactive Features:

  • • Select Distribution - Choose from 6 different distributions
  • • Adjust Parameters - Change distribution parameters with sliders
  • • Toggle CDF - Show/hide cumulative distribution function
  • • Explore Values - See probability at specific x values

What You'll See:

  • • PMF/PDF Graph (green) - Probability mass/density function
  • • CDF Graph (blue, dashed) - Cumulative distribution function
  • • Point Marker (orange) - Selected x value
  • • Properties Panel - Mean, variance, standard deviation

Number of successes in n independent trials

PMF

Probability at x = 0

PMF

0.0000

P(X = x)

CDF

0.0000

P(X ≤ x)

Distribution Properties

Mean (μ)

NaN

Expected value

Variance (σ²)

NaN

Measure of spread

Std Dev (σ)

NaN

Square root of variance

Key Concepts

PMF (Discrete): Probability Mass Function - P(X = x) for discrete random variables

PDF (Continuous): Probability Density Function - f(x) for continuous random variables

CDF: Cumulative Distribution Function - P(X ≤ x) or F(x)

Mean: Expected value, center of the distribution

Distribution Applications

Binomial: Coin flips, success/failure experiments

Poisson: Rare events, arrivals, counts

Geometric: Waiting times, first success

Normal: Natural phenomena, measurement errors

Uniform: Equal probability, random selection

Exponential: Time between events, decay processes

Lessons

Individual learning units

Lessons coming soon

Probability Distribution - Function, Formula, Table | Maths Learning