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This article explains the concept of probability distributions, describes the Gaussian (normal) distribution with its parameters, demonstrates how to visualize it using Python code, and discusses random variables, independence, and real‑world examples such as atmospheric CO₂ time‑series data.
This article introduces Monte Carlo methods, explains how random sampling approximates integrals, discusses uniform and non‑uniform probability distributions, and details acceptance‑rejection sampling as a technique for generating samples from complex distributions, laying the groundwork for understanding Markov Chain Monte Carlo in AI.
Monte Carlo methods, originally a gambling-inspired random simulation technique, provide a versatile way to approximate integrals and sums, and by using acceptance‑rejection sampling they enable drawing samples from complex probability distributions, a key step toward effective Markov Chain Monte Carlo algorithms in machine learning and AI.