Choose a Distribution
Understanding Probability Distributions
A probability distribution describes how likely different outcomes are for a random variable. There are two main types:
- Continuous distributions (Normal, Uniform, Exponential) — described by a Probability Density Function (PDF). The area under the curve represents probability.
- Discrete distributions (Binomial, Poisson) — described by a Probability Mass Function (PMF). Each bar shows the probability of that exact value.
When to Use Each Distribution
| Distribution | Use When... | Examples |
|---|---|---|
| Normal | Data clusters around a mean, symmetric | Heights, test scores, measurement errors |
| Binomial | Counting successes in fixed trials | Coin flips, defect counts, pass/fail |
| Poisson | Counting events in time/space intervals | Customer arrivals, typos per page |
| Uniform | All values equally likely in a range | Random number generators |
| Exponential | Time between independent events | Wait times, equipment lifetime |
Frequently Asked Questions
What's the difference between PDF and PMF?
PDF (Probability Density Function) is for continuous variables — you find probabilities by calculating areas under the curve. PMF (Probability Mass Function) is for discrete variables — you read probabilities directly from the bar heights.
Why is the normal distribution so important?
The Central Limit Theorem states that the sum of many independent random variables tends toward a normal distribution, regardless of the original distributions. This makes it fundamental in statistics.
How do I know which distribution to use?
Consider your data: Is it continuous or discrete? Bounded or unbounded? Symmetric or skewed? Does it count events or measure quantities? The table above can guide your choice.
Privacy & Limitations
- All calculations run entirely in your browser -- nothing is sent to any server.
- Results are computed using standard formulas and should be verified for critical applications.
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Probability Distribution Visualizer FAQ
What is Probability Distribution Visualizer?
Probability Distribution Visualizer is a free math tool that helps you Visualize normal, binomial, Poisson, and other probability distributions.
How do I use Probability Distribution Visualizer?
Enter your input values, review the calculated output, and adjust inputs until you reach the result you need. The result updates in your browser.
Is Probability Distribution Visualizer private?
Yes. Calculations run locally in your browser. Inputs are not uploaded to a server by default, and refreshing the page clears session data.
Does Probability Distribution Visualizer require an account or installation?
No. You can use this tool directly in your browser without sign-up or software installation.
How accurate are results from Probability Distribution Visualizer?
This tool applies standard formulas or deterministic processing logic for estimates. For medical, legal, tax, or investment decisions, verify with a qualified professional.
Can I save or share outputs from Probability Distribution Visualizer?
You can bookmark this page and copy outputs manually. Results are not persisted in your account and are typically not embedded in the URL.