Calculator Inputs
Example Data Table
| Distribution | Inputs | Formula Type | Sample Output | Use Case |
|---|---|---|---|---|
| Normal | μ = 50, σ = 8, x = 54 | 0.044009 | Exam score modeling | |
| Uniform | a = 2, b = 12, x = 6 | 0.100000 | Equal interval likelihood | |
| Exponential | λ = 0.4, x = 3 | 0.120478 | Waiting time analysis | |
| Binomial | n = 10, k = 4, p = 0.5 | PMF | 0.205078 | Quality pass counts |
| Poisson | λ = 2.5, k = 3 | PMF | 0.213763 | Arrival count modeling |
Formula Used
The calculator supports both continuous density functions and discrete mass functions. Continuous models return density heights, while discrete models return exact point probabilities.
- Normal: f(x) = [1 / (σ√(2π))] · exp(-(x-μ)² / (2σ²))
- Uniform: f(x) = 1 / (b-a), for a ≤ x ≤ b; otherwise 0
- Exponential: f(x) = λe−λx, for x ≥ 0
- Binomial: P(X = k) = C(n,k)pk(1-p)n-k
- Poisson: P(X = k) = (λke−λ) / k!
It also reports the model mean and variance to help compare central tendency and spread across different distributions.
How to Use This Calculator
- Select the probability distribution matching your problem.
- Enter the evaluation point x for continuous models or count k for discrete models.
- Provide the required parameters, such as μ, σ, λ, a, b, n, or p.
- Press the calculate button to display the result above the form.
- Review the density or probability value, support, formula, mean, variance, and interpretation.
- Use the CSV and PDF buttons to export the displayed result summary.
Frequently Asked Questions
1. What does this calculator return?
It returns either a probability density value for continuous models or a probability mass value for discrete models, plus mean, variance, support, and interpretation.
2. Why can a density value be greater than one?
A density is not a direct probability at one exact point. Probability comes from the area under the curve across an interval.
3. When should I use the normal option?
Use it when the variable is continuous, roughly symmetric, and described well by a bell-shaped curve around a mean.
4. What is the difference between binomial and Poisson?
Binomial counts successes across a fixed number of trials. Poisson counts events in a fixed interval using an average rate.
5. What happens if x is outside the support?
For supported models like uniform or exponential, the calculator returns zero whenever the evaluation point lies outside the allowed range.
6. Can I export my result?
Yes. Use the CSV button for spreadsheet-friendly output or the PDF button for a printable summary of the result table.
7. Is this suitable for study and professional work?
Yes. It is useful for homework, exam practice, model checking, and quick probability verification during analysis or reporting tasks.