论文标题
完成集合所需的优惠券的平均值和差异
The mean and variance in coupons required to complete a collection
论文作者
论文摘要
本文是关于优惠券收藏家的问题。有一些优惠券，棒球卡，或其他塑料刀柄，它们放入薯片袋或苏打水瓶下等。收藏家开始收集这些小饰品，并希望形成所有可能的饰品。但是，每次购买产品时，他们都不知道他们将“收集”哪种优惠券，直到打开产品。在完成收藏品之前，他们需要收集多少张优惠券？在本文中，我们使用各种方法探讨了此随机变量的均值和差异，$ n $。其中一些仅适用于特殊情况，因为优惠券具有同等的收集概率，而另一些则将其推广到以不平等概率收集优惠券（更接近现实世界情景）的情况下。
This paper is about the Coupon collector's problem. There are some coupons, or baseball cards, or other plastic knick-knacks that are put into bags of chips or under soda bottles, etc. A collector starts collecting these trinkets and wants to form a complete collection of all possible ones. Every time they buy the product however, they don't know which coupon they will "collect" until they open the product. How many coupons do they need to collect before they complete the collection? In this paper, we explore the mean and variance of this random variable, $N$ using various methods. Some of them work only for the special case with the coupons having equal probabilities of being collected, while others generalize to the case where the coupons are collected with unequal probabilities (which is closer to a real world scenario).
