Quiz dashboard
The bank contains 180 questions across 30 probability distributions and six matching formats.
Quiz settings
Interactive distribution explorer
Change the example distribution and parameters. The graph updates immediately.
Distribution comparison guide
| Comparison | Main distinction | Selection clue |
|---|---|---|
| Binomial vs Poisson | Fixed trials versus event counts in an interval. | Use binomial for known n and Poisson for a rate. |
| Geometric vs Negative Binomial | First success versus a specified number of successes. | Check the stopping rule. |
| Hypergeometric vs Binomial | Without replacement versus independent trials. | Look for a finite population correction. |
| Normal vs Student's t | Normal tails are lighter. | Use t for small samples with unknown variance. |
| Exponential vs Weibull | Exponential has constant hazard. | Use Weibull when failure risk changes over time. |
| Gamma vs Chi-square | Chi-square is a special gamma family member. | Degrees of freedom signal chi-square. |
| Beta vs Dirichlet | One proportion versus a vector of proportions. | Dirichlet components sum to one. |
| Normal vs Log-normal | Unbounded symmetric values versus positive skewed values. | Take logs to test log-normal behaviour. |
| Normal vs Cauchy | Cauchy has much heavier tails and undefined moments. | Extreme outliers and unstable averages suggest Cauchy. |
| Poisson vs Zero-inflated Poisson | Ordinary counts versus extra structural zeros. | Compare observed and expected zero frequencies. |
How to use the quiz
- Choose a mode, difficulty, family, and question count.
- Start the quiz and match each clue with a distribution.
- Use hints carefully because they reduce weighted scores.
- Bookmark difficult questions for a focused review session.
- Finish the quiz to generate Plotly performance reports.
- Export the detailed review as CSV or print it as PDF.
Frequently asked questions
How many questions are included?
The quiz contains 180 generated questions. Each distribution receives six distinct matching formats.
Are the questions randomized?
Question order and answer order can both be randomized. Disable either setting before starting.
What does Learn Mode change?
Learn Mode displays supporting parameters and structural clues. It still records answers and performance.
How does Match Challenge work?
Each round presents five clues and five names. Every correctly matched pair earns credit.
How are hints scored?
A correct answer receives a reduced weighted score after using a hint. Accuracy remains based on correctness.
What happens in Survival Mode?
You begin with three lives. An incorrect answer removes one life and zero lives end the attempt.
Can progress be saved?
Yes. Progress, bookmarks, and incorrect-question history are stored in the browser.
Can I review only mistakes?
Select Review Incorrect before starting. The mode loads questions previously answered incorrectly.
Do the graphs show exact fitted data?
The explorer uses representative parameterized examples. It is intended for learning distribution shapes.
Can results be exported?
Results can be copied, downloaded as CSV, or printed through the browser as PDF.
Does the quiz work on mobile devices?
Yes. Controls, cards, charts, and matching interactions adapt to smaller screens.