Probability and Statistics
概率论与数理统计是人工智能与数据科学的核心数学基础，研究随机现象的规律性与统计推断方法。课程内容包括随机事件与概率、随机变量及其分布、数字特征、大数定律与中心极限定理、参数估计、假设检验、回归分析等。学生将培养概率思维与数据分析能力，为机器学习、贝叶斯推断、统计学习等后续课程提供理论支撑。
Probability and Statistics is a core mathematical foundation for AI and data science, studying the regularity of random phenomena and statistical inference methods. Topics include probability, random variables and distributions, numerical characteristics, the law of large numbers, the central limit theorem, parameter estimation, hypothesis testing, and regression analysis. The course develops probabilistic thinking and data analysis skills, supporting machine learning, Bayesian inference, and statistical learning.
学生需基于贝叶斯定理实现一个朴素贝叶斯分类器，对真实数据集（如鸢尾花或新闻文本）进行分类。要求完成数据预处理、先验与条件概率估计、预测及评估等环节，并与sklearn基准对比准确率。需提交代码、实验报告及可视化结果，讨论平滑策略与特征独立性假设的影响。
Students implement a Naive Bayes classifier based on Bayes' theorem to classify real datasets such as Iris or news text. The project covers data preprocessing, prior and conditional probability estimation, prediction, and evaluation, comparing accuracy with sklearn baselines. Deliverables include code, a report with visualizations, and discussion of smoothing strategies and the feature independence assumption.