I am not able to understand the solution of part iv and v. anyone please explain the concept behind this and how we arrived at answer
You've not been very specific about which parts of the solution to (iv) and (v) you don't understand, so it's very difficult to help you. Broadly speaking, part (iv) is testing the whether there is a difference in rates between males and females. No difference corresponds to k = 1 (as then the value of xi doesn't matter), and a difference corresponds to k is not equal to 1. This gives the hypotheses. The test uses the properties of maximum likelihood estimators that you should know from CT3: - they are unbiased (so the expected value is the true underlying value) - the variance is equal to the CRLB (given on page 23 of the Tables) - they are normally distributed. Part (v) relies on the definition of the median, which you should again recall from CT3, and knowledge of the Nelson-Aalen method from Chapter 8. Note that this approach is not something I've seen in the exam before.
