How do I simulate an exam-score curve?

Open this page and use the live Bayesian Workbench tool below — set your inputs and the simulation runs instantly in your browser using real numerics. No install, no account needed.

Yes. The simulation runs free in your browser. A one-time unlock or a Pro plan adds advanced parameters, saved presets, data import, and clean exports.

Can I use my own numbers?

Absolutely — every input is adjustable, and with data import you can drive an exam-score curve from your own measurements.

Use case · powered by Bayesian Workbench

Bayesian Workbench for an exam-score curve

Simulate an exam-score curve live in your browser. This runs the real Bayesian Workbench solver — adjust the inputs, watch it respond instantly, and export the result. No install, no account.

For:Students Researchers Educators Engineers Hobbyists & Makers K-12 Students First Responders

Bayes Inference

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Bayesian InferenceLive

prior × likelihood → posterior

Controls

Presets

Prior α (pseudo-heads)

Prior β (pseudo-tails)

Observed heads

Observed tails

Bayesian inference updates a prior belief with data to form a posterior. For a coin, a Beta prior combined with binomial coin flips gives a Beta posterior — the conjugate update is just adding heads to α and tails to β. Watch the posterior sharpen and shift as evidence accumulates.

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Data Inspector

Posterior mean0.667

Posterior SD0.094

Posterior α, β16.0, 8.0

Governing equation

p ∣ data \sim Beta (α + h, β + t) = Beta (16.0, 8.0), E [p] = \frac{α + h}{α + β + n} = 0.667

Reading this result: The posterior mean 0.667 sits between the prior mean 0.500 and the observed rate 0.700; with 20 flips versus 4.0 pseudo-counts, the data dominates and pulls the estimate toward the evidence.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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Monte Carlo

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Monte Carlo Price SimulationLive

geometric Brownian motion

Controls

Presets

Initial price S₀

Expected return μ

Volatility σ

Horizon (years)

Geometric Brownian motion models a price with constant drift and random volatility — the assumption behind Black-Scholes. Running hundreds of simulated paths reveals the full distribution of outcomes, not just an average. Educational tool, not investment advice.

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Data Inspector

Median outcome$0

5th percentile$0

95th percentile$0

Governing equation

S_{t + Δ t} = S_{t} e^{(0.07 - \frac{0. 2 ^{2}}{2}) Δ t + 0.2 Δ t Z}, \tilde{S}_{1} \approx $0

Reading this result: Median outcome is about $0, just under the drift-only $107 — GBM compounds in log-space, so volatility always pulls the typical path below the average.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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Bootstrap

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Bootstrap ResamplingLive

confidence without formulas

Controls

Presets

Original sample size

Bootstrap resamples B

The bootstrap estimates uncertainty by resampling your data with replacement thousands of times and recomputing the statistic each time. The spread of those bootstrap means gives a confidence interval — no formula or normality assumption required. Powerful when the math is intractable.

▶ Run in Python

Data Inspector

Sample mean0.00

95% CI low0.00

95% CI high0.00

CI width0.00

Governing equation

\hat{θ}^{*} = \frac{1}{25} i = 1 \sum 25 x_{i}^{*}, CI_{95%} = [\hat{θ}_{(2.5%)}^{*}, \hat{θ}_{(97.5%)}^{*}] = [0.00, 0.00]

Reading this result: The spread of the resampled means is the confidence interval — no normality assumption needed. Sample size sets its width; more resamples only sharpen its edges.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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About this simulation

The full Bayesian Workbench tool models an exam-score curve with the same numerics engineers and scientists use — running entirely client-side. Change any parameter and the result updates in real time, so you can build intuition, check a design, or teach the concept without spreadsheets or installs.

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Other ways to simulate an exam-score curve

Optimize + UQ for an exam-score curve Hypothesis Test for an exam-score curve Linear Regression for an exam-score curve Central Limit Theorem for an exam-score curve Confidence Intervals for an exam-score curve Bayesian Inference for an exam-score curve

Frequently asked questions

How do I simulate an exam-score curve?: Open this page and use the live Bayesian Workbench tool below — set your inputs and the simulation runs instantly in your browser using real numerics. No install, no account needed.
Is it free?: Yes. The simulation runs free in your browser. A one-time unlock or a Pro plan adds advanced parameters, saved presets, data import, and clean exports.
Can I use my own numbers?: Absolutely — every input is adjustable, and with data import you can drive an exam-score curve from your own measurements.