Inthispaper,weconsiderthestationaryprobabilityandfirst-passagetimeofbiasedrandomwalkon1Dchain,whereateachstepthewalkermovestotheleftandrightwithprobabilitiespandqrespectively(0p,q1,p+q=1).Wederiveexactanalyticalresultsforthestationaryprobabilityandfirst-passagetimeasafunctionofpandqforthefirsttime.Ourresultssuggestthatthefirst-passagetimeshowsadoublepower-lawF~(N-1)~γ,wheretheexponentγ=2forN<|p-q|~(-1)andγ=1forN>|p-q|~(-1).Ourstudyshedsusefulinsightsintothebiasedrandom-walkprocess.
