概率理论的自然介绍

English | PDF | 2003 | 196 Pages | ISBN : 3764321881 | 14.3 MB

According to Leo Breiman (1968), probability theory has a right and a left hand. The right hand refers to rigorous mathematics, and the left hand refers to 'proba­ bilistic thinking'. The combination of these two aspects makes probability theory one of the most exciting fields in mathematics. One can study probability as a purely mathematical enterprise, but even when you do that, all the concepts that arise do have a meaning on the intuitive level. For instance, we have to define what we mean exactly by independent events as a mathematical concept, but clearly, we all know that when we flip a coin twice, the event that the first gives heads is independent of the event that the second gives tails. Why have I written this book? I have been teaching probability for more than fifteen years now, and decided to do something with this experience. There are already many introductory texts about probability, and there had better be a good reason to write a new one. I will try to explain my reasons now.

根据Leo Breiman (1968)的观点，概率论有“右手”和“左手”。右手指的是严格的数学理论，“左手”则指的是“概率思维”。将这两方面结合起来，使得概率论成为数学领域中最令人兴奋的学科之一。人们既可以将概率论作为一种纯粹的数学研究对象，但即使如此，在直觉层面上所有出现的概念仍然都有其意义。例如，我们必须精确地定义作为一个数学概念的独立事件的意义，但是很明显的是，当我们翻两次硬币时，第一次得到 heads 的事件与第二次得到 tails 的事件是独立的。我为什么要写这本书呢？我已经教概率论超过15年了，并决定利用这些经验去做一些事情。关于概率论已有许多入门书籍，有必要撰写新的书籍一定有很好的理由。我现在就试着解释一下我的理由吧。

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