Kindly address all the questions
An investigation has been performed into risk factors for liver disease in persons currently resident in the United Kingdom (UK) and aged over 50 years. It considered the impact of three covariates: age at the start of the investigation, wockly alcohol consumption and previous residence in a tropical country. The investigation used a Cox regression model for the hazard of developing the disease, h(f), with three parameters, PA, Pc, and Pr, as follows: *(!) = h,(1)exp(B, 4+ BcC+B,T). A was defined as exact age at the start of the investigation less 50 years. Crepresented weekly alcohol consumption, and took the value 1 if the person consumed more than the recommended maximum per week (a heavy drinker) and 0 otherwise. T represented previous residence in a tropical country, and took the value 1 if the person had lived in a tropical country for more than 12 months and 0 otherwise. (1) State the characteristics of a person to whom the baseline hazard, ho(!), applies. [1] The results of the investigation revealed that the hazard was: twice as high for a heavy drinker aged 60 years exact at the start of the investigation than for a person aged 50 years exact at the start of the investigation who was not a heavy drinker, where neither had previously lived in a tropical country. four times as high for a heavy drinker who had previously lived in a tropical country for more than 12 months than for a non-heavy drinker of the same age who had not previously lived in a tropical country. three times as high for a person who had lived in a tropical country for more than 12 months than for a person of the same age and drinking habits who had always lived in the UK. (ii) Calculate 34. BC, and By- [5] The probability of a person aged 50 years exact at the start of the investigation, who does not drink heavily and has always lived in the UK remaining free of the disease for 10 years is 0.8. (iii) Show that the probability of a person of the same age and drinking habits, who has lived for more than 12 months in a tropical country, remaining free of the disease for 10 years is slightly over one half. [4] [Total 10]An insurance portfolio contains policies for three categories of policyholder: A, B and C. The number of claims in a year. N. on an individual policy follows a Poisson distribution with mean A. Individual claim sizes are assumed to be exponentially distributed with mean 4 and are independent from claim to claim The distribution of 2., depending on the category of the policyholder, is Category Value of A Proportion of policyholders 20% 60%% 20% Denote by S the total amount claimed by a policyholder in one year. (i) Prove that E(S) - E[E(SA)]- [2] (ii) Show that E.(S )) =42 and Var(S [2)=323. [2] (iii) Calculate E(S). [2] (iv) Calculate Var( $). [2] [Total 8] The following information is available for a motor insurance portfolio: The number of claims settled: Development Year Accident year 2006 442 151 50 2007 623 111 2008 681 The cost of settled claims during each year (in 000's): Development Year Accident year 2 2006 6321 1901 701 2007 7012 2237 2008 7278 Claims are fully run off after year 2. Calculate the outstanding claims reserve using the average cost per claim method with grossing up factors. Inflation can be ignored
