Makinguseofaneasiermethod,thispaperderivestheprobabilitydensityfunction(pdf)ofthelinearcombinationofrandomvariableZ=αX+βY.Furthermore,cumulativedistributionfunction(cdf)ofZ=αX+βY,whereXandYhavethebivariateexponentialdistributions,hasalsobeenproposedinthispaper.Resultsfromthispaperwouldhaveimportantroleinthereliabilitystudy.