Let T be a survival time with hazard rate α(t), and let v > 0 be a constant. If we consider the survival time T conditional on T > v, we say that the survival time is left-truncated. a) Show that the...

Let T be a survival time with hazard rate α(t), and let v > 0 be a constant. If we consider the survival time T conditional on T > v, we say that the survival time is left-truncated.

a) Show that the left-truncated survival time has a hazard rate that equals zero on the interval [0,v] and equals
 and determine the intensity process of the counting process

Let
 be constants, and consider the left-truncated and right-censored survival time
 obtained by censoring the left-truncated survival time at u > v, and let

b) Determine the intensity process of the counting process