= Solution
Applying <death-only rate correction under exponential censoring> to the death fraction and combined-rate estimate, \b[the corrected plug-in death rate is]
$$
\boxed{\widehat\lambda_{\text{plug-in}}
=\frac23\times0.3=0.2\ \text{year}^{-1}.}
$$
The corresponding censoring-rate estimate is $0.1\ \text{year}^{-1}$. This correction is consistent under the <independent> exponential competition model: the death-only conditional rate estimates $s$ and the observed fraction estimates $\lambda/s$.
There is an important distinction from the full-data <maximum-likelihood estimate>. If $T_D$ and $T_C$ are total observed follow-up for the 100 deaths and 50 censored subjects, the full likelihood for both rates is
$$
L(\lambda,\gamma)\propto\lambda^{100}\gamma^{50}
e^{-(\lambda+\gamma)(T_D+T_C)},
\qquad
\boxed{\widehat\lambda_{\mathrm{full}}=\frac{100}{T_D+T_C}.}
$$
The reported death-only rate determines $T_D=100/0.3$, but supplies no $T_C$, so the exact full-data estimate cannot be reconstructed from the numerical summaries alone. The value $0.2$ is the requested corrected rate using those summaries; it need not equal the realised full-data maximum-likelihood estimate. The full analysis should use the actual censored follow-up whenever available.
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