Learn the principles behind AI — properly

NumLM explains probability, statistics, machine learning and large language models from first principles — with formulas you can follow, worked examples, and experiments whose results are published as they happen.

Lessons in English

Descriptive Statistics

Coefficient of Variation

The coefficient of variation (CV) is a relative measure of spread equal to the standard deviation divided by the mean; because the units cancel, it is a…

Descriptive Statistics

Skewness

Skewness is a standardized third-moment statistic that measures how far a data distribution departs from left–right symmetry (it is a defined term in the…

Probability Distributions

Poisson Distribution

The Poisson distribution is a discrete probability distribution for the number of rare, independent events that occur in a fixed interval of time or space…

Probability Distributions

Law of Large Numbers

The law of large numbers is a fundamental theorem of probability stating that as the number of independent trials n increases, the sample mean converges to…

Machine Learning

Association Rules and Anomaly Detection

Association rule learning is an unsupervised learning task that finds patterns of items appearing together — such as "customers who buy A also buy B" —…

Probability Distributions

Normal Distribution

The normal distribution is a symmetric, bell-shaped continuous probability distribution centered on its mean μ, with probability density function f(x) =…

Probability Distributions

Central Limit Theorem

The central limit theorem (CLT) states that when independent samples of sufficiently large size n are drawn from a population with mean μ and variance σ²,…

Probability

Bayes' Theorem: The Core Idea

Bayes' theorem is the conditional-probability rule P(A|B) = P(B|A)P(A)/P(B), which tells you how to update a prior probability P(A) into a posterior…

inference

The p-Value

A p-value is the probability, assuming the null hypothesis is true, of obtaining a test statistic at least as extreme as the one observed; it ranges from 0…

Inferential Statistics

Confidence Interval

A confidence interval is an interval estimate constructed so that, if the same sampling procedure were repeated many times, a specified proportion of the…

Public experiment

Can AI predict lottery numbers?

Statistical, LSTM, Transformer and ensemble models each publish 100 combinations before every Korean Lotto 6/45 draw. After the draw they are scored against random picks and the theoretical baseline — and the cumulative record is never edited.

See the results

Everything else is in Korean

The full curriculum — hundreds of concept pages and 46 interactive labs — is written in Korean. Your browser can translate it: in Chrome, right-click the page and choose “Translate to English”. We add English pages based on what readers actually use.

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