Answer the questions

1 An insurer is setting the premium rate for the buildings in an industrial estate. Past experience fo the estate indicates that a premium rate of f3 per f1,000 sum insured should be charged. The past experience of other similar estates for which the insurer provides cover indicates a premium rate of f5 per f1,000 sum insured. If the insurer uses a credibility factor of 75% for this risk, calculate the premium rate per f1,000 sum insured. 2 Claim amounts on a portfolio of insurance policies have an unknown mean / . Prior beliefs about yle / are described by a distribution with mean / and variance on . Data are collected from n daims with mean claim amount x and variance s" . A credibility estimate of / is to be made, of the form: Zx + (1-2)/0 Suggestions for the choice of Z are: no A noo + 52 B noo noo +n C n+ go Explain whether each suggestion is an appropriate choice for Z. 3 The total claim amount per annum on a particular insurance policy follows a normal distribution tyle with unknown mean @ and variance 200. Prior beliefs about @ are described by a normal distribution with mean 600 and variance 50" . Claim amounts x1, *2,...., x, are observed over n years. (i) State the posterior distribution of 0. (ii) Show that the mean of the posterior distribution of @ can be written in the form of a credibility estimate. Now suppose that n= 5 and that total claims over the five years were 3,400. (iii) Calculate the posterior probability that O is greater than 600..4 A large industrial company recruits a constant number of school leavers aged exactly 13 years on 1 July each year. Upon joining1 workers undergo training for one year. Of those who complete this period. of training1 ten per cent fail a nal tat of competence and are dismissed. Employees may also leave service voluntarily at any time. The central rate of voluntary withdrawal from service is {115 for trainees and U'J'U' at each age for fully trained employees. The occupation is hazardous and all workers1 including trainees1 are exposed to the risk of injury. The independent qtype rate of injury is ll at age 13 and at ages 19 and above. An employee who is injured is transfeITed to alternative work with a subsidiary company1 at a relocation cost of 311%. The mortality of all employees follows English Life Tables No.12 Males. The number of employees attaining age 21 each year is 513-0. {i} Construct a service table covering the rst 3 years of employment with the original com pany1 distinguishing between those about to take the nal test of competence and those who pass it. [Regard failing the test as a special mode of decrement ] {ii} How many people are recruited on each 15t July