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概率在證明恒等式和不等式中的應(yīng)用
概率在證明恒等式和不等式中的應(yīng)用
摘要：概率論的思想已廣泛應(yīng)用于其它學(xué)科，用概率論中的方法解決其它學(xué)科中的1些問題是1個(gè)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(lián)系以及應(yīng)用概率論方法解題的美妙之處．應(yīng)用的基本思路是：根據(jù)所要解決的問題，首先構(gòu)造1個(gè)適當(dāng)?shù)母怕誓Ｐ停缓髴?yīng)用概率中的已知結(jié)論解決所討論的問題．如何構(gòu)造適當(dāng)?shù)母怕誓Ｐ褪墙鉀Q問題的難點(diǎn)所在，也是關(guān)鍵所在．
關(guān)鍵詞：隨機(jī)變量；數(shù)學(xué)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
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