Characterizations of Distributions by Conditional Expectation

• Main Authors: Tao-Wen Chang, 張道文
• Other Authors: Mong-Na Lo
• Format: Others
• Language: en_US
• Published: 2001
• Online Access: http://ndltd.ncl.edu.tw/handle/70683141217043339211

碩士 === 國立中山大學 === 應用數學系研究所 === 89 === 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.