****************************************************** PR # 11147 We selected optically bright high z QSO's considering that X-ray intensities of QSO's eventually correlates with optical brightness. It is possible for us to estimate ASCA count rates assuming the correlation between X-ray and optical intensities. This assumption is based on the past X-ray observations of QSO's. The z dependence of spectral index is expected from a Compton reflection model of X-ray spectrum.It is essential for CXB to understand the spectral structure of QSO's with z= 2 to 4. ******************************************************