Statistics & Probability
Distributions, sampling, the central limit theorem, confidence intervals, and hypothesis tests — live histograms you can resample
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Central Limit Theorem
Pick a parent (uniform, exponential, binomial, die), draw samples of size n = 1, 5, 30; the histogram of means turns normal and its sprea…
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Normal Distribution & z-Scores
Bell curve with μ and σ; shaded tails, the 68–95–99.7 rule, and a built-in z-score converter x → z = (x − μ)/σ.
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Galton Board (Bean Machine)
Balls bounce left/right through rows of pegs; the bins fill a binomial that turns into a bell curve. Few rows vs many rows.
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Binomial Distribution
P(K = k) bars for n trials with success p; mean np, variance np(1−p); coin and rare-event presets; normal overlay at large n.
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Law of Large Numbers
Coin or die: running mean x̄ₙ for several runs converges to μ; the ±σ/√n envelope shows how slowly.
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Confidence Interval Simulator
Draw a sample, build a 90/95/99 % interval for μ; repeat 100 times and count how many intervals catch the true mean.
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p-Value Explained
Test statistic on the null density; shaded one- or two-sided tail is the p-value. Why it is not the probability that H₀ is true.
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Type I & II Errors and Statistical Power
Two normal curves (H₀ and H₁), a decision threshold; α, β and power 1−β as shaded areas; effect size, σ and n sliders.
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Pearson Correlation
Scatter cloud with adjustable r, covariance ellipse, and a parabola preset where r ≈ 0 despite a perfect relationship.
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Bayes' Theorem: Medical Test Paradox
Sensitivity, specificity and prevalence on a 2×2 population grid; why a positive test can still mean a low chance of disease.