probability-theory
Mathematical foundations of uncertainty and random phenomena. Covers sample spaces, events, axioms, conditional probability, Bayes' theorem, independence, random variables, distributions (discrete and continuous), expected value, variance, the law of large numbers, and the central limit theorem. Use when computing probabilities, reasoning about random events, working with probability distributions, or building the foundation for statistical inference.
Profile →npx skills add majiayu000/claude-skill-registry --skill probability-theory --agent claude-code
Same command for any agent — swap --agent for codex, cursor, copilot.
Weekly change comes from our own snapshots, not the repository page — it measures attention, not adoption.
# Probability Theory Probability is the mathematical language of uncertainty. It provides the axiomatic foundation on which all of statistical inference rests: without probability, there is no hypothesis testing, no confidence intervals, no Bayesian updating, no regression. This skill covers the core machinery from sample spaces through the central limit theorem. **Agent affinity:** bayes (conditional probability, Bayes' theorem), pearson (distributional theory), efron (computational probability) **Concept IDs:** stat-probability-foundations, stat-experimental-theoretical, stat-expected-value, stat-conditional-probability ## Axioms and Sample Spaces ### Kolmogorov's axioms A probability function P on a sample space S satisfies: 1. **Non-negativity:** P(A) >= 0 for every event A. 2. **Normalization:** P(S) = 1. 3. **Countable additivity:** For mutually exclusive events A_1, A_2, ..., P(A_1 union A_2 union ...) = P(A_1) + P(A_2) + ... Everything in probability follows from these three axioms plus set theory. ### Sample space and events - **Sample space (S):** The set of all possible outcomes of a random experiment. - **Event (A):** A subset of S. "The die shows an even number" = {2,
- Axioms and Sample Spaces
- Kolmogorov's axioms
- Sample space and events
- Counting and equally likely outcomes
- Conditional Probability
- Definition
- The multiplication rule
- The law of total probability
- Bayes' Theorem
- Independence
- Random Variables and Distributions
- Discrete random variables
- Continuous random variables
- The CDF
What does the probability-theory skill do?
Mathematical foundations of uncertainty and random phenomena. Covers sample spaces, events, axioms, conditional probability, Bayes' theorem, independence, random variables, distributions (discrete and continuous), expected value, variance, the law of large numbers, and the central limit theorem. Use when computing probabilities, reasoning about random events, working with probability distributions, or building the foundation for statistical inference.
How do I install it?
Run `npx skills add majiayu000/claude-skill-registry --skill probability-theory --agent claude-code` — it drops the skill into your project so the agent can pick it up. Swap the --agent value for codex, cursor or copilot if you use one of those.
Where does this skill come from?
From majiayu000/claude-skill-registry, a repository with 534 stars. We read it straight from the repository tree rather than a submitted listing, so what you see here is what is actually published.
Is a popular skill a good skill?
Not necessarily. Stars measure attention, not adoption — a repository can trend for a week and be abandoned. That is why we show the weekly change from our own snapshots next to the total, instead of a single flattering number.