关于概率论中近似计算问题的几点标记

Some Marks on Approximate Calculation Problem in Probability Theory

概率的近似计算是常见且重要的问题,运用加法公式、泊松定理和中心极限定理等理论工具,对概率的取值范围和随机变量的近似分布等问题进行近似计算并辅以实例说明,其中利用切比雪夫不等式理解“3σ”法则、超几何分布近似二项分布和Stirling公式的证明具有创新性。通过所列举的例题,可以体现出概率论中近似计算思想的重要性,由此可见概率近似计算在教学实践与理论创新中具有一定的意义。

The approximate calculation of probability is a common and important problem.Using theoretical tools such as additive formulas, Poisson′s theorem and central limit theorem theory, this paper makes approximate calculations of the range of probability values and the approximate distribution of random variables with examples.Among them, it is innovative to use Chebyshev′s inequality understanding of the "3σ" rule, the Hypergeometric distribution approximate Binomial distribution and the proof of Stirling formula.The importance of approximate calculation in probability theory can be shown by the corresponding examples, which shows that approximate calculation of probability has certain reference significance in teaching practice and theoretical innovation.