4. (3 marks) As part of a study into duration of unemployment a number of individuals who recently lost their job were observed for some time. The table below provides the observed, possibly censored (indicated with a +) and truncated, survival times (in months) where time 0 corresponds to the time of becoming unemployed and the event of interest is the acquirement of a new job. Also recorded and displayed are the age of each person and whether he she had a job in the service or manufacturing industry before becoming unemployed. recorded survival time (0,3] (6,15+] (1,7] (2,8+] (4,10] (0,20+] age 18 30 40 25 45 60 type of last job (s-service S S job, m=manufacturing job) For modelling the duration of unemployment set up a Cox proportional hazards model with age and type of last job acting as the covariates and provide an explicit expression in terms of the two regression coefficients for the partial likelihood given the above data. (You should clearly define each piece of notation that you use.)