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所在平台: Udemy |
课程主页: https://www.udemy.com/course/random-variables-and-probability-distributions/
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**课程名称：** 随机变量与概率分布 **课程概述：** 本课程旨在深入讲解随机变量和概率分布的基础知识及其在实际应用中的重要性。 **第一部分：概率分布基础** * **变量与随机变量的区别：** 区分普通变量和随机变量的概念。 * **离散与连续随机变量：** 介绍离散和连续随机变量的定义、特征及其异同。 * **概率分布的必要性：** 阐述为何需要概率分布来描述随机现象。 * **离散概率分布：** 讲解离散概率分布的基本概念、特性和定义。 * **连续概率分布：** 讲解连续概率分布的基本概念、特性和定义。 * **概率分布的图形表示：** 通过直方图和连续函数等图形化方式，直观展示概率分布的特征。 * **案例研究：** 配以简单的案例研究，帮助理解每个概念的实际应用。 **第二部分：重要离散概率分布** * **二项分布 (Binomial Distribution)：** * 适用条件。 * 数学函数推导。 * 均值和标准差（方差）。 * 实际应用案例。 * **几何分布 (Geometric Distribution)：** * 适用条件。 * 数学函数推导。 * 均值和标准差（方差）。 * 实际应用案例。 **第三部分：正态分布** * **正态分布 (Normal Distribution)：** 介绍正态分布的概念。 * **标准正态分布 (Standard Normal Distribution)：** 讲解标准正态分布（Z值/Z曲线）及其意义。 * **概率计算：** 如何计算标准正态分布和正态分布下的概率。 * **正态性检验：** 如何判断样本数据是否符合正态分布。 * **正态概率图 (Normal Probability Plot)：** 介绍正态概率图及其用途。 * **数据转化：** 当样本不符合正态分布时，如何进行数据转化使其趋于正态。 * **正态近似：** 利用正态分布近似计算离散概率分布的概率。 **第四部分：概率基础（可选参考）** 本部分为选修内容，旨在帮助缺乏概率论基础的学习者巩固相关概念。 * **概率基础概念：** 解释机遇试验、样本空间、事件、可能性等基本定义。 * **重要概率定理：** * 条件概率 (Conditional Probability)。 * 贝叶斯定理 (Bayes Theorem)。 * **概率性质。**
The first section focuses onProbability distributions Starts with identifying the difference between a variable and a random variable. Explains discrete and continuous random variables and their characteristics. Move on to explain the need for the probability distributions. explains the basics, characteristics and definitions around the discrete probability distribution and continuous probability distributions. explains the graphical representations of probability distributions involving histograms and continuous functions Every aspect is illustrated with a simple case study to appreciate the detailsThe second section focusses ontwo important discrete probability distributions namely Binomial distribution & Geometric distribution Explains - the conditions to be met for each of these experiments - derivation of mathematical functions that describe these distributions - mean and standard deviation (variance) for each of these distributions - applications of these distributions in certain real world using examplesThe third section explains What is a Normal distribution? What is a standard Normal distribution ( z value / z curve )? How are probabilities evaluated for a standard Normal distribution and normal distribution? How to judge if a sample data is Normally distributed? What is a normal probability plot? How to transform data into a normal distribution when the sample is not? How to arrive at probabilities for a discrete probability distribution using normal approximations?Section four is only for reference and is OPTIONALAdded here in order to help those who do not have the pre-requisite knowledge on essential concepts on probabilityExplains the basic underlying concepts and definitions on probability involving, Chance experiments, Sample Space, Events, LikelihoodTwo important theorems on probability namely- Conditional probability and- Bayes theoremVarious properties on Probability
