基于全期望公式的随机红包算法分析

Analysis of Random Red Envelope Algorithm Based on Full Expectation Formula

介绍了应用随机过程课程中随机变量的条件数学期望满足的一个等式——全期望公式,并利用全期望公式对随机红包金额生成算法进行分析.通过对随机红包金额的期望、方差及一些相关事件发生的概率进行计算以解决平时人们对随机红包感兴趣的最大和最小等问题,进一步用Matlab软件进行模拟实验,并将计算机模拟实验结果与计算结果进行比较验证.本文以实际问题引入知识点,达到既加深对知识点的全面理解,又能运用知识解决实际问题的目的.

This paper introduces an equation in the course of applying stochastic processes that the conditional mathematical expectation of random variables satisfies,that is the full expectation formula,and uses it to analyze the random red envelope amount generation algorithm.By calculating the expectation and variance of the amount of random red envelopes and the probability of some related events to solve the maximum and minimum problems that people are interested in random red envelopes,using the software Matlab to simulate the experiment and comparing the results with the calculated results to verify the conclusion.Knowledges are introduced by a practical problem,so as to deepen the comprehensive understanding of the knowledge and to apply the knowledge to solve practical problems.