Past exam of the mathematics course of the University of Cambridge / 2003 / iii / Paper 40 / 1 / b / i / Solution

Write $X=\min (T,c)$ and $\Delta =1_{\{T\le c\}}$ for the right-censored survival time and observed-failure indicator. Since the exponential distribution is continuous, including or excluding equality at $c$ makes no difference. Using the tail-integral expression for an expectation,Consequently the expected integrated hazard at the observed endpoint satisfiesAdministrative censoring therefore stops both the accumulated exposure and the opportunity to record a failure.