#probability

Topics tagged "probability".

• Random Walk

  A path built by adding up independent random steps; its typical distance from the start grows like the square root of the number of steps.

• Probability Distribution

  A complete description of how likelihood is spread across the possible outcomes of a random quantity.

• Central Limit Theorem

  The sum or average of many independent random quantities tends to a normal distribution, no matter what shape the individual quantities have.

• Law of Large Numbers

  As you collect more independent samples, their running average converges to the true expected value.

• Markov Chain

  A random process that hops between states where the next state depends only on the current one, forgetting all earlier history.

• Probability & Random Processes

  How randomness, far from being formless, organizes itself into sharp and predictable structure — bell curves, steady states, and laws of large numbers.

• Brownian Motion

  The continuous-time limit of a random walk — the erratic, jittery path traced by a particle buffeted by countless tiny random kicks.

• Benford's Law

  In many natural collections of numbers the leading digit is 1 about 30% of the time, not 11% — a logarithmic bias that holds across populations, areas, and physical constants.

• Anscombe's Quartet

  Four small datasets engineered to share almost every summary statistic — mean, variance, correlation, and regression line — yet look completely different when plotted. A warning that numbers without a picture can lie.

• Monte Carlo Method

  Estimate a hard quantity by generating many random samples and averaging the results.

• Bayes' Theorem

  A rule for updating the probability of a hypothesis as new evidence arrives.

• Galton Board

  A board of pegs that turns a stream of falling balls into a bell-shaped pile — the central limit theorem made physical.