Statistics tutorials and worked examples

Calculate conditional probabilities and test distribution assumptions.

• Bernoulli vs binomial: one outcome or a count of trials

  Calculate and simulate a binomial count, relate it to Bernoulli trials and test what fails when outcomes share a common cause.

  tutorial · 4 min read

• Conditional probability with a table: change the denominator

  Calculate P(flagged | faulty) and P(faulty | flagged) from a small inspection table, then connect them through Bayes’ rule.

  tutorial · 4 min read

Interpret entropy and distribution mismatch with explicit calculations.

• Entropy, cross entropy and KL divergence on the same distribution

  Calculate uncertainty, coding mismatch and KL divergence in nats, verify their identity and inspect a zero-probability failure.

  tutorial · 4 min read

Use intervals and resampling while keeping their assumptions visible.

• Bootstrap confidence intervals: work through every resample

  Enumerate a small bootstrap distribution, calculate a percentile interval and explain what its uncertainty does and does not represent.

  tutorial · 4 min read

Interpret evidence under an explicit null model.

• P-values explained with an exact coin-test calculation

  Calculate a two-sided binomial p-value, define what counts as extreme, and separate evidence against a model from effect size and practical importance.

  explanation · 4 min read

Check plots, comparisons and conclusions against the underlying values.

• Misleading statistics: 7 examples and how to spot each one

  Seven common ways true numbers mislead: truncated axes, missing denominators, base rates, Simpson's paradox, survivorship bias, cherry-picked windows and correlation sold as cause. With a checklist for reading any claim.

  explanation · 11 min read

Build the foundations for evaluating models and experiments.

• Statistics and probability for data science and machine learning: what to learn, in order

  The statistics and probability a data scientist or machine learning engineer uses, in a seven-step order: what each step covers, a worked example for each, and what to skip.

  learning path · 6 min read