概率在證明恒等式和不等式中的應用

時間：2024-07-22 03:38:37 數學畢業論文我要投稿

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概率在證明恒等式和不等式中的應用

摘要：概率論的思想已廣泛應用于其它學科，用概率論中的方法解決其它學科中的1些問題是1個非常有趣的課題．本文利用概率論中方法證明恒等式和不等式，從中可看出它們之間的聯系以及應用概率論方法解題的美妙之處．應用的基本思路是：根據所要解決的問題，首先構造1個適當的概率模型，然后應用概率中的已知結論解決所討論的問題．如何構造適當的概率模型是解決問題的難點所在，也是關鍵所在．

關鍵詞：隨機變量；數學期望；方差；恒等式；不等式

The applications of probability theory in the
proofs of equalities and inequalities

Abstract: The thought of probability theory has already been applied to many other subjects extensively. It is very interesting to solve some problems in other subjects by using probability theory. In this paper, some methods in probability theory are used to prove several equalities and inequalities in Mathematics. By this, we can see the close relationship between them. It is also very valid to solve problems by using probability theory. Our method is as follows: according to the problem, we first construct their proper probability models, then use some known conclusions in probability theory to solve them. How to construct their probability models is the difficult point as well as the key point.

Key words: random variable; mathematical expectation; variance; equality; inequality

概率在證明恒等式和不等式中的應用

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