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彩票发行方案的优化

时间:2017-08-11 数学毕业论文 我要投稿

目   录
摘要 1
1 彩票发行问题的背景 3
2 彩票的分类及设奖规则 4
2.1 “传统型”彩票 4
2.2 “乐透型”彩票 4
2.3 发行彩票的设奖规则 5
3 提出模型要解决的问题 7
3.1 提出彩票方案需解决的问题 7
3.2 模型参数的基本假设 7
3.3 彩票各种奖项出现的可能性分析 7
4 建立彩票模型 11
4.1 1等奖期望模型 11
4.2 彩票模型的最终建立 12
4.2.1 建立彩票模型的准备 12
4.2.2 确定吸引力函数 14
4.2.3 彩票模型的建立 15
4.2.4 对各方案合理性的分析 15
4.2.5 彩票模型的求解 16
5 模型评价及改进意见 19
5.1 模型评价 19
5.2 模型改进意见 19
参考文献 20
致谢词 21
附录 22


摘    要
本设计旨在建立关于彩票发行方案的数学模型,分析现有的29种彩票发行方案的合理性,并以设定的函数为标准,设计1种更好的方案。
针对 “传统型”和“乐透型”两种彩票各奖项中奖概率,计算各方案每种奖项奖额的期望。先考虑各奖项的1等奖的期望,建立1个比较简单的1等奖期望模型。然后再综合考虑1、2、3等奖的金额,中1等奖的概率、中2、3等奖的总概率、中4至7等奖的总概率6个方面,构造吸引力函数,分析各方案对彩民的吸引力,求出对彩民吸引力较大的方案。综合分析“乐透型”彩票和“传统型”彩票中各方案的合理性;结合“乐透型”彩票中的最优方案的优点并以此为基础,限定取值范围搜索最优值,改进其各奖项奖额,在此的基础上给出1种更好的方案。
关键词:彩票方案;中奖概率;头奖期望;吸引力。          

Abstract
In this design we will seek for the mathematic model of an attractive lottery ticket scheme. We analyze the rationality of 29 kinds of lottery ticket schemes and then establish a better scheme based on the objective function.
This design studies the ratio of getting the winning number in lottery in “Traditional type” and “Too happy type” lottery tickets respectively. Firstly, it calculates the expectation value of various of the first-class prize amount and we study the sum of winning the first-class, the second –class and third-class prizes, winning the first-class’s probability, the total probability of the second –class and third-class prizes, the total probability of the fifth-class, sixth-class and seventh-class, we adopt a quantitative description-“attraction” of lottery schemes and reach a conclusion which model is more appealing to buyers. Integrate analyze rationality of the “Traditional type ” and “Too happy type” lottery tickets ;According to the excellence of “Too happy type” lottery model , and at the base of this model, Limit the worth of scope and search for the superior value, Improve its each prize sum, at base of this model to give a kind of better project.
Keywords: Lottery ticket project; Win a prize all rate; First prize expectation; Attraction

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