摘要
依据随机性的基本特征,结合案例分析创设数学情景,用数学建模思维感悟数学模型建立的过程.突显依概率收敛、大量随机现象平均结果的稳定性、独立同分布随机变量中心化三个概率模型的支撑作用,实现从概率直觉思维、抽象思维到创新思维的分层推进,领会切比雪夫不等式、大数定律与中心极限定理之间的内在联系.
Based on the basic characteristics of randomness, combined with Buffon ’ s needle injection experiment, a mathematical scenario was created, and the mathematical modeling thinking is used to understand the process of establishing mathematical models.The three probability models of probability convergence, the stability of the average results of a large number of random phenomena,and the centralization of independent and identically distributed random variables are highlighted as the support points to realize the hierarchical advancement from probabilistic intuitive thinking, abstract thinking, to innovative thinking, and understand the intrinsic connections among Chebyshev inequalities, law of large numbers and the central limit theorem.
作者
赵云
ZHAO Yun(Department of Mathematics,Gansu Normal College for Nationalities,Hezuo Gansu 747000)
出处
《甘肃高师学报》
2022年第5期5-9,共5页
Journal of Gansu Normal Colleges
基金
2021年甘肃省教育科学“十四五”规划重点课题“基于MOOC的概率论与数理统计教学模式的探索与实践”(1883)
2022年甘肃省高校创新创业教育教学改革研究项目“以创新创业教育为导向的《概率论与数理统计》课程实践教学研究”
2022年甘肃民族师范学院校长科研重点项目“基于数据分析素养的数理统计教学研究”(GSMYZD2022-01)。
关键词
蒲丰投针实验
概率模型
大数极限定律
中心极限定理
Buffon needle injection test
probability model
limit law of large numbers
central limit theorem
