About Probability Distribution Simulator & PMF/CDF Lab
Interactive statistical probability workbench for discrete and continuous stochastic models. Simulate Binomial distributions (n trials, p success), Poisson processes (rare events with rate λ), and Exponential decay models. Features dynamic probability mass function (PMF) charts and expected value readouts.
Key Capabilities & Features
- Multi-model simulation: Binomial (n, p), Poisson (λ), and Exponential (λ)
- Interactive parameter sliders with instant probability mass function (PMF) bar chart updating
- Hover tooltips displaying exact probability P(X = k) for every discrete outcome
- Automatic computation of theoretical expected value E[X], variance Var(X), and standard deviation
- Publication-grade responsive SVG visualization optimized for educational and research use
How to Use Probability Distribution Simulator & PMF/CDF Lab
Select Probability Model
Choose between Binomial, Poisson, or Exponential distributions.
Adjust Model Parameters
Use sliders to modify trials n, success probability p, or arrival rate λ.
Explore Probability Bars
Hover over outcome bars to inspect exact point probabilities P(X = k).
Evaluate Theoretical Moments
Review expected values and variance metrics for the simulated process.
Privacy & In-Browser Execution Guarantee
100% Client-Side. Stochastic models and combinatorial calculations execute locally in JavaScript.
Frequently Asked Questions
When is a Poisson distribution used instead of a Binomial distribution?
The Poisson distribution models the count of rare events occurring in a fixed interval of time or space when the number of trials n is large and probability p is small, satisfying λ = np.
What is the memoryless property of the Exponential distribution?
The Exponential distribution is the only continuous distribution with memorylessness, meaning P(X > s + t | X > s) = P(X > t); the probability of an event occurring in the future is independent of past elapsed time.