 Solution

A right-censored subject contributes survival up to the recorded censoring time, not no information. Under independent censoring, write $x_i=\min (T_i,C_i)$ and $v_i=1_{\{T_i\le C_i\}}$. For exponential death rate $\lambda$, the event-model survival likelihood isDiscarding censored subjects drops observed exposure and selects people whose death occurred before censoring. Their recorded event times are not an unselected sample of all death times. The death-only conditional distribution can differ from the marginal death-time distribution even when censoring is independent. A correct maximum-likelihood estimate uses the total observed person-time, including censored follow-up.