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Distributions

The normal distribution, binomial distribution, t-distribution, z-scores, and the empirical rule — the shapes that real-world data actually takes.

15 articles

Illustration: Every value in the interval is equally likely, so probability is just proportional width

Sep 25, 20267 min read

The Uniform Distribution: Formula, Worked Examples, and When to Use It

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Illustration: Small samples give the t-distribution heavier tails than the normal

Sep 24, 20267 min read

The T-Distribution vs. the Normal Distribution: What Actually Differs

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Illustration: Multiplicative growth gives a right-skewed curve: the mean sits above the median

Sep 19, 20268 min read

The Log-Normal Distribution: When Logarithms Are Normal

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Illustration: Events per interval when the average rate is λ = 4; mean and variance are both 4

Sep 5, 20267 min read

Poisson Distribution: Formula, Worked Examples, and Real-World Uses

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Illustration: The shape parameter k sets whether failure rates fall, stay flat, or wear out

Sep 3, 20267 min read

The Weibull Distribution: Modeling Wear-Out and Reliability

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Illustration: The CDF at x is the area under the PDF to its left: here F(0.8) = 0.788

Aug 31, 20267 min read

PDF vs. CDF: Two Ways to Describe the Same Distribution

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Illustration: The F(5, 20) curve; the shaded right tail past 2.71 is the 5% rejection region

Aug 29, 20267 min read

The F-Distribution: The Shape Behind ANOVA and the F-Test

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Illustration: Twelve trials with a 35% success rate; the highlighted bars add up to P(X ≤ 4)

Aug 27, 20267 min read

Binomial Distribution: Formula, Worked Examples, and the Normal Approximation

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Illustration: Ten voters, three parties (50 / 30 / 20%): the chance of the split 5–3–2 is 0.085

Aug 20, 20267 min read

The Multinomial Distribution: When There Are More Than Two Outcomes

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Illustration: Trials needed to reach the 3rd success at p = 0.4 — a geometric wait, repeated

Aug 12, 20267 min read

The Negative Binomial Distribution: Waiting for the R-th Success

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Illustration: Waiting time between random events: 63% of waits are shorter than the mean

Aug 9, 20267 min read

The Exponential Distribution: Modeling Wait Times and Lifetimes

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Aug 7, 20268 min read

Normal Distribution: The Bell Curve, Explained

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Illustration: Trials until the first success, at p = 0.3: each extra failure is a little less likely

Aug 6, 20267 min read

The Geometric Distribution: Trials Until the First Success

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Illustration: A z-score counts how many standard deviations a value sits from the mean

Aug 5, 20268 min read

Z-Score: Formula, Worked Examples, and How to Read One

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Illustration: Drawing 10 from 50 without replacement (bars) vs. with replacement (rings): a tighter spread

Aug 3, 20268 min read

The Hypergeometric Distribution: When Sampling Without Replacement Really Matters

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Mean, median, mode, standard deviation, variance, quartiles and the interquartil…

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Basic probability rules, conditional probability, Bayes' theorem, expected value…

Sampling & Inference

Sampling distributions, the Central Limit Theorem, standard error and confidence…

Hypothesis Testing

Null and alternative hypotheses, p-values, Type I/II errors, t-tests, chi-square…

Regression & Correlation

Pearson correlation, simple and multiple linear regression, R², and residual ana…

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Exploratory data analysis, data visualization, A/B testing, and Bayesian statist…

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