The article walks through a simple two‑box, four‑ball example to illustrate basic probability, conditional probability, joint probability, and then reverses the conditioning to derive Bayes’ theorem, showing each step with concrete calculations and visual partitions of the sample space.
This article explores the Beta distribution’s role in Bayesian statistics, detailing its definition, properties, conjugate prior relationship, and practical examples such as coin flips and bus arrivals, illustrating how it simplifies probability updates and supports intuitive belief revision.
This article explains how the law of large numbers and the central limit theorem underpin Monte Carlo methods, revealing why their convergence rate is low, how significance and confidence levels are defined, and why variance reduction is crucial for efficient simulations.
This article explains the Beta distribution’s definition, its probability density and cumulative distribution functions, key statistical properties such as mode, mean, variance, skewness and kurtosis, and illustrates its practical use in modeling relative humidity in atmospheric studies.
This article explains the Gamma distribution and its inverse, detailing their probability density functions, expectations, variances, special cases, and how the Gamma distribution relates to Poisson and exponential distributions, providing concise mathematical insights and reference sources.
The article explains how normal (Gaussian) distributions underpin many machine‑learning algorithms, reviewing the central limit theorem, multivariate Gaussian sampling, and key properties such as products, sums, conditional and marginal distributions, linear transformations, and Gaussian‑based Bayesian inference.
By drawing analogies between casino gambling and SSD garbage collection, the article uses probability theory, Brownian motion, and stochastic processes to model victim block selection, resource depletion, and I/O bandwidth fluctuations, proposing control strategies that balance performance stability and resource safety.
