The following table gives a small data set of survival times: patient id survival time (in years)
1 11.3
2 12.7+
3 10.2
4 9.8
5 12.1+
6 7.8
Where + means a right censored observation. Suppose f(t)=λexp(-λt) follows the exponential distribution.
1) give the likelihood function based on the above data.
2) calculate the maximum likelihood estimator of λ.