Kindly help in answering the following economic questions.

Question 14.5 List the factors that could lead to an increase in the supply of Good X.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 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]The following model for the force of mortality for a life insurance company's annuitants has been proposed: u(1,1) = (0.015 -0.00017).exp[a(x; - 70) + B.y, + 7.z; ] where: #(1, i) = force of mortality for the ith life, in calendar year 2000 + / ; x; = age of the ith life; y; = 1 if the ith life is a smoker, or y; = 0 if a non-smoker; z, = 1 if the ith life is male, or z, =0 if female; and or, B, y are the parameters of the model. The following data have been observed over the calendar year 2003: Risk characteristics Number of annuitants Number dying Male non-smoker, average age 65 800 Male smoker, average age 60 200 Female non-smoker, average age 70 450 Female smoker, average age 65 150 You can assume that the numbers of annuitants in each class remained constant throughout the investigation period, and that the average age for each class can be treated as representing the value of x; for each individual in that class. Explain why this model is a proportional hazards model. [2] (ii) Explain the importance of subdividing the data by age, sex and smoking status, and explain whether you think each of the parameters a, / and y would be likely to be positive or negative. [3] (iii) Calculate the force of mortality for female non-smokers with average age 70 in 2007, according to this model. [1] (iv) (a) Obtain an expression for the partial likelihood based on the given data, expressing your answer in terms of a, S and y only. (b) State how you would estimate the parameters of the model using the partial likelihood. [6] [Total 12]