Learn how to generate samples of both discrete and continuous random variables by mapping uniformly distributed numbers onto target distributions, with step-by-step explanations, probability tables, and Python NumPy code that simulates events and computes frequencies for large-scale experiments.
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 the key numerical characteristics of random variables—including expectation, variance, covariance, correlation, and higher-order moments such as skewness and kurtosis—explains their definitions, properties, and relationships, and extends these concepts to random vectors and matrix representations.
This article explains the fundamentals of probability, conditional probability, independent events, the law of total probability, and both discrete and continuous probability distributions, including joint and marginal densities and conditional distributions for random variables.
