6. For the Poisson distribution with probability mass function Pr( X = j) = e-adj ?! ' ] = 0, 1 , 2 , .... Show that the hazard function is monotone increasing. Q6 For j E NU {0}, the hazard function is given by 1 h ( j ) := P{X = j} _ e-dy P{X 2 j} which is positive for all j for any A > 0. So, we can consider for any je NU {0}, h(j + 1) h(j ) (j+1)!> >ijne dri/i! Zij edxi/i! Zizie-Axili! = j+1_;edit/(i+1)! >(i+De-xx/(i+ 1)! 2 Ex, (i+ 1)e-AN/(i+1)! = 1. Therefore, h(j + 1) 2 h(j) for all je NU {0}, i.e. h(j) is monotonic increasing on NU {0}