1.Suppose we have a small data set with different kinds of censoring:2, 3+, 4, 5, 6-, 7+, [8, 9], where + means right censoring, - means left censoring, and [a,b] means interval censoring.Suppose the distribution of the underlying survival time is an exponential distribution with a constant hazard .Write down the likelihood function of for this given data set.

2.For the following small data set of survival time:3, 4+, 5, 6, 6+, 8+, 11+, 14, 15, 16+, do the following (assume the underlying failure times are from a Weibull distribution):

a.Write down the log-likelihood function of the data

b. Find the score and information matrix from this model and then evaluate them under the hypothesis that the data are from an exponential distribution.

c.Perform the score test to test whether or not the survival times are from an exponential distribution.