Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 207 / 4 / b / vi

Proton and Prune are censored after the estimated survivor curve has already crossed one half. Learning their later death times may add jumps in the far tail but cannot change the first crossing, so the nonparametric median remains seven years. An exponential distribution instead estimates one constant hazard from the total event count divided by total time at risk. Replacing censoring by observed later deaths changes both quantities and therefore changes the fitted rate and its median $\log 2/\hat{\lambda }$.