DETAIL: You work for an insurer, Indigo Insure, and have been tasked with developing an innovative insurance that will cover building defects on new houses and commercial buildings. Arising from the pyrite and mica problems in Ireland, your boss thinks that demand for an insurance like the one proposed will have a strong latent demand. The policy will be called HOME PROTECT and will be available for houses built after 2020 whether they are for owner/occupiers or landlords- also, builders may acquire the insurance and offer it in support of a construction guarantee. The limit will be a maximum of Euro 100,000 on any single building. It will protect against and will pay for the costs of poor workmanship, defective design or poor materials. Information and data available to you includes: a review of 250 houses suggests a 0.05 chance of any construction having an issue. () the sample suggests costs of repair, adjusted for inflation, follow the pattern below.. (ie, these are the only possible claim sizes) 25,000 25,000 25,000 38,000 38,000 69,000 80,000 100,000. Question 1: (a) statistically summarise and comment on the claims information provided and determine a basic premium, (ii) looking at the indicated frequency rate, how confident are you that this is reliable? (b) it is anticipated that 600 insurance will be sold in a year: find the total risk premium (ii) find the standard deviation (iii) assuming 20% is added to the total risk premium for costs, what is the probability of incurring total losses beyond 2,000,000; hence what is the likelihood of having three such years in five ? (c) find the cost of a stop loss reinsuring beyond 40 losses (d) Assuming only a total loss for 100,000 can occur, and that a policyholder has a 100,000 policy limit, where the utility to house value is U= V, what is the maximum premium that can be charged?.