本研究探讨了基于交互式模拟的硬币试验在数理统计中的应用。首先，通过设计基于 RStudio 框架的硬币抛掷模拟应用程序，使用了交互式模拟工具 Shiny 实现了对硬币试验的直观展示。其次，通过模拟实验、绘制图表和数据 分析，加深了对大数定律和中心极限定理的理解。进一步，运用贝叶斯推断 和概率模型，使用似然函数来探索了不均匀硬币特性的推断方法，为统计推 断提供了新的视角。最后，结合蒙提霍尔问题的模拟和贝叶斯定理的运用， 拓展了对贝叶斯统计在决策问题中的应用认识。这项研究为学生提供了一个 实践数理统计理论的平台，同时也为教学实践和理论研究提供了新的思路和方法。

This study investigates the utilization of interactive simulation-based coin toss experiments in mathematical statistics. Firstly, by designing a coin toss simulation application based on the RStudio framework, it utilizes the interactive simulation tool Shiny to achieve an intuitive presentation of coin experiments. Through simulation experiments, chart plotting, and data analysis, it delves into the principles of the law of large numbers and the central limit theorem, enhancing comprehension of these fundamental statistical concepts. Additionally, by employing Bayesian inference and probability models, it investigates inference techniques for identifying biased coins' characteristics using likelihood functions, introducing novel approaches to statistical inference. Moreover, by integrating simulations of the Monty Hall problem and applying Bayesian theorem, it broadens the scope of Bayesian statistics in decision-making scenarios. This study not only offers a platform for students to practically engage with theoretical concepts in mathematical statistics but also presents innovative ideas and methodologies for both teaching practices and theoretical inquiries.