TABLE OF CONTENTS Estimation of the probability P( A ? X+ B ? Y+ C>0) and its particular cases under the assumption of normality was the subject of investigations by Enis and Geisser (1971), Pensky (1982), Gupta and Gupta (1990) and Ivshin and Lumelskii (1993, 1994) among others. Ivshin and Lumelskii (1994) study unbiased estimation of P( A ? X+ B ? Y+ C>0) and its generalization when N ?2 independent normal vectors are given. Pensky (1982) constructed an UMVUE of P( A ? X+ C>0). Gupta and Gupta (1990) studied a particular case of estimating P( A ?X+ C>0) with C=0: their model is written as P( A ? X> B ?Y), however the normally distributed vectors X and Y are assumed to be dependent, so that these two vectors can be combined into a single vector X. Enis and Geisser (1971) derived the Bayes estimator of P( A ?X+ C>0) based on a noninformative Jeffreys's prior for C=0. Several authors studied the MLE and the UMVUE of P(X< Y) when (X, Y) is a two-dimensional random vector, among them Mukherjee and Sharan (1985) and Roy (1993). Below, we shall apply the general theory developed in the previous section to obtain the MLE, the UMVUE and the Bayes estimator of R= P( A
