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所在平台: Udemy |
课程主页: https://www.udemy.com/course/probability-and-statistics-maam/
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Coursera课程“概率与统计”内容概览： 本课程深入浅出地讲解了概率论与统计学的核心概念。 **概率部分**： * **概率基本性质**：涵盖了概率的基本规则、公理以及现实世界中的应用。 * **枚举方法**：介绍了排列（permutations）和组合（combinations）等计数技巧，是高效解决计数问题的关键。 * **条件概率**：讲解了在获得额外信息的情况下，概率如何发生变化。 * **独立事件**：深入探讨了事件之间完全不受影响的情况。 * **贝叶斯定理**：这是一个强大的工具，用于根据新证据更新概率，并介绍了其在不同领域的实际应用。 **离散分布部分**： * **离散随机变量**：介绍了离散随机变量及其在建模现实世界现象和统计分析中的重要性。 * **数学期望**：解释了期望值及其在概率论中的意义。 * **主要离散概率分布**：包括二项分布（Binomial）、超几何分布（Hypergeometric）、负二项分布（Negative Binomial）和泊松分布（Poisson），并附有实际应用示例。 **连续分布部分**： * **连续随机变量**：讨论了连续随机变量，重点介绍了概率密度函数（probability density functions）和累积分布函数（cumulative distribution functions）。 * **常见连续概率分布**：涵盖了指数分布（Exponential）、伽马分布（Gamma）、卡方分布（Chi-Square）和正态分布（Normal），解释了它们的性质、应用以及在数据科学中的相关性。 **双变量分布部分**： * **离散与连续双变量分布**：探讨了分析两个变量之间关系的离散和连续双变量分布。 * **相关系数**：介绍了衡量关系强度的相关系数（Correlation Coefficient）。 * **条件分布**：描述了在给定条件下概率的分布情况。
PROBABILITYThis section covers the fundamental Properties of Probability, including basic rules, axioms, and real-world applications. It explores different Methods of Enumeration, such as permutations and combinations, essential for solving counting problems efficiently. The concept of Conditional Probability is introduced, explaining how probabilities change with additional information. Independent Events are discussed in depth, highlighting cases where events do not influence each other at all. Finally, the section includes Bayes' Theorem, a powerful tool for updating probabilities based on new evidence, along with practical applications in various fields.DISCRETE DISTRIBUTIONSThis section introduces Discrete Random Variables and their importance in modeling real-world phenomena and statistical analysis. Mathematical Expectation is covered, explaining expected values and their significance in probability theory. It explores key discrete probability distributions, including the Binomial, Hypergeometric, Negative Binomial, and Poisson Distributions, with real-world examples that illustrate their practical uses.CONTINUOUS DISTRIBUTIONSThis section discusses Continuous Random Variables, emphasizing probability density functions and cumulative distribution functions. It covers the Exponential, Gamma, Chi-Square, and Normal Distributions, explaining their properties, applications, and relevance in data science.BIVARIATE DISTRIBUTIONSThis section examines Discrete and Continuous Bivariate Distributions, methods for analyzing relationships between two variables, the Correlation Coefficient, which measures relationship strength, and Conditional Distributions, describing probability distributions under given conditions.
