本文所探討的是關於以條件期望值刻劃分佈. 首先以條 X≦y 替代Huang and Su (2000) 中的條件 X ≧ y, 並給定存在一隨機變數 X 滿足 E(g(X) | X ≦y)=h(y)
f(y) / F(y), " y Î CX 的充要條件, 其中CX 表 X 取值的範圍. 此外我們也將此結果推廣至二變量的情況 .

In this thesis, first we replace the condition X ≦ y in Huang and Su (2000) by X ≧ y and give necessary and sufficient conditions such that there exists a random variable X satisfying that E(g(X)| X ≦ y)=h(y) f(y )/ F(y), " y Î CX, where CX is the support of X.Next, we investigate necessary and sufficient conditions such that h(y)=E(g(X) | X ≦ y ), for a given function h and extend these results to bivariate case.

1.Introduction

2.Characterization of univariate random variable by a relationship between
the conditional expectations and the probability density function

3.Characterization based on the conditional expectations of functions

4.Bivariate case

5.References

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