Question 4. You implement the Cox model to investigate how some factors affect the lifetime of retired school teachers. You look at the influence of gambling addiction on the life time. The table below represents survival times for 6 teachers with the same start age. The teachers are labelled as 'censored' if they leftthe observation and we have no further information about them since. In the Cox model you consider that Z = 1 for gamblers and Z = 0 for non-gamblers. Initially, the only parameter of the model is . Teacher 1 2 3 Years to death alive Gambler (yes/no) No Censored Yes 7 No No 8 No Yes 10 4 5 6 9 3 (a) [5 marks] Write down the expression for the partial likelihood. Yes Yes No No Yes No (b) [5 marks] Find the maximum partial likelihood estimate *.