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Probability Distributionscontinuous and discrete random variables and their corresponding probability distributions. Probability functions, probability densities and (cumulative) distribution functions are introduced. Transformations of random variables are discussed, with particular attention given to the cases where the iOffbeat 发表于 2025-3-22 01:18:12
Special Continuous Probability Distributionsterizing the decay of unstable atoms and nuclei, the ubiquitous normal (Gauss) distribution in both its general and standardized form, the Maxwell velocity distribution in its vector and scalar form, the Pareto (power-law) distribution, and the Cauchy (Lorentz, Breit–Wigner) distribution suitable foemission 发表于 2025-3-22 06:25:58
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Stable Distributions and Random Walkse closely related to the simple convolution process, which is introduced first for continuous and then for discrete random variables. This leads to the central limit theorem as one of the most important results of probability theory, as well as to its generalized version which is useful in the analy沙发 发表于 2025-3-22 20:46:20
Statistical Inference from Samplesdomly drawn from a population. The concepts of the statistic and the estimator are introduced, paying attention to their consistency and bias. Sample mean and sample variance are defined, and three most relevant sample distributions are investigated: distribution of sums and differences, distributio小歌剧 发表于 2025-3-22 22:30:05
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Statistical Tests: Verifying Hypothesesr probability distributions. The null and alternative hypothesis are the corner-stones of each such verification, and go hand-in-hand with the possibility of inference errors; these are defined first, followed by the exposition of standard parametric tests for normally distributed variables (tests o