Past exam of the mathematics course of the University of Cambridge / 2004 / iii / Paper 38 / 2 / a / i / Solution

Use the paper's notation $F$ for the survivor function, not for a cumulative distribution function. For a nonnegative continuous event time,The hazard function is defined where survival is positive, and the last expression is the integrated hazard. These definitions assume the usual absolutely continuous survival distribution so that the displayed density and hazard derivatives exist almost everywhere.