论文标题
重新访问两个孩子问题的名称变体
Revisiting the name variant of the two-children problem
论文作者
论文摘要
最初是由马丁·加德纳（Martin Gardner）在1950年代提出的，著名的两个孩子问题通常被视为概率理论的悖论。这个悖论的一个相对较新的变体指出，在一个两个孩子的家庭中，至少一个孩子是一个女孩，另一个孩子是男孩的可能性为$ 2/3 $，但如果披露女孩的名字的名字，这种概率会变成$ 1/2 $（前提是两个姐妹可能没有给出相同的名字）。我们重新审视了这个问题的这种变体，并表明，如果一个人采用自然模型以给女孩的名字命名的方式，那么另一个孩子是男孩的可能性可能会在$（0,2/3）$中获得任何值。通过利用Schur-Concavity的概念，我们研究了这种概率如何取决于模型参数。
Initially proposed by Martin Gardner in the 1950s, the famous two-children problem is often presented as a paradox in probability theory. A relatively recent variant of this paradox states that, while in a two-children family for which at least one child is a girl, the probability that the other child is a boy is $2/3$, this probability becomes $1/2$ if the first name of the girl is disclosed (provided that two sisters may not be given the same first name). We revisit this variant of the problem and show that, if one adopts a natural model for the way first names are given to girls, then the probability that the other child is a boy may take any value in $(0,2/3)$. By exploiting the concept of Schur-concavity, we study how this probability depends on model parameters.
