随机序列的子集是否也是随机的? [英] Is a subset of a random sequence also random?

问题描述

给出:

• 随机数序列
• X个客户从序列中选择Y个数字，形成他们自己的子序列
• 控制选择过程的规则未知

是否有一个数学特性可以保证每个客户最终得到一个随机的数字序列?也就是说，无论选择过程如何，是否也可以保证随机序列的子集是随机的?

Is there a mathematical property that guarantees that each client will end up with a random sequence of numbers? That is, is a subset of a random sequence also guaranteed to be random regardless of the selection process?

更新:我正在尝试确定是否可以使用单个随机数生成器向多个客户端分配值:

UPDATE: I was trying to establish if I could use a single random-number generator to dish out values to multiple clients: Do stateless random number generators exist? -- That is, clients choose elements from the sequence without replacement. That being said, I was wondering about the general case as well (when the selection rules are not known).

推荐答案

随机数序列"中的随机"一词通常被解释为表示从该序列中没有任何关于序列中任何元素的附加信息序列中的任何其他元素. (即元素X _{i 先验和后验概率分布} >在研究其他任何元素之前和之后都是相同的.)

The word "random" in "a sequence of random numbers" is generally construed to mean that there is no additional information about any element of the sequence from looking at any other elements of the sequence. (i.e. the a priori and a posteriori probability distributions of element X_i are the same before and after studying any of the other elements.)

只要多个客户都没有使用任何数字，就可以了. (正如其他人提到的那样，在您看清其价值之后，您不能决定接受其中一项.)

As long as none of the numbers are used by more than one client, you should be fine. (edit: and as others have mentioned, you can't decide to accept one of the elements after you look at its value.)

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