Respond to the questions below explaining each question appropriately.

William. aged TS. and Laura aged 30. are the guardians of a child. They take out an annual premium life assurance policy that provides a payment of 25,000 payable immediately when the last guardian dies. {i} State the conditions under which premiunu would normally be payable. [1] [ii] State with reasons which. if any, of the guardians' litres should he examined medically. [ll {iii} Calculate the premium, assuming that premium payments are limited to a maximum of 10 years. the medical examinations were satisfactory and the lives are subject to PA92C20 mortality. Assume 4% pa interest and allow for expenses of 5% of each premium and an initial expense of 250. [9] [Total n] You have been asked to advise a sports magazine, as a consultant statistician. You have been asked to investigate the hypothesis that football managers in the Italian "Serie A", are dismissed more quickly than those in the English premier league. Each league has twenty teams, each with one manager. During the season the following events happened (at the end of the months indicated) to the twenty managers who started: Month Italy England 1 One dismissed One died One left of his own accord 5 One left of his own accord One dismissed 6 Two dismissed One left of her own accord 8 One died Two dismissed 11 Two dismissed One dismissed Hence there were thirteen of the original twenty managers still employed by the same club at the end of the season, for each of the two leagues. (i) Calculate the Kaplan-Meier estimate of the distribution function and its approximate variance for each league separately. [10] (ii) Comment on the hypothesis that Italian managers are dismissed more quickly than those in England. [2] [Total 12]