The following data consists of the times to relapse and the times to death following relapse of 10 bone marrow transplant patients. In the sample patients 4 and 6 were alive in relapse at the end of the study and patients 7-10 were alive, free of relapse at the end of the study. Suppose the time to relapse had an exponential distribution with hazard rate A and the time to death in relapse had a Weibull distribution with parameters 6 and a. Patient Relapse Time Death Time (months) {months) 1 5 11 2 8 12 3 12 15 k! 24 337 5 32 45 6 7 28" 7 167 16* 8 17" 17 9 197 19* 10 307 307 * Censored observation (a) Construct the likelihood for the relapse rate A. (b) Construct a likelihood for the parameters 6 and a. (c) Suppose we were only allowed to observe a patients death time if the patient relapsed. Construct the likelihood for 6 and a based on this truncated sample, and compare it to the results in (b)