Question 4, Answer all parts of the question The risk manager for a fleet of delivery lorries has studied the pattern of vehicle damage over the past few years and has produced the following probability distribution: Annual cost of losses (s) 0 16,000 16,001-32,000 32,001-80,000 80,001- 160,000 160,001-320,000 320,001-800,000 800,001- 1,600,000 Probability .15 .3 .25 .15 .08 .05 .02 An insurance company has quoted an insurance premium of 120,000 to cover all of the risk REQUIRED (showing all workings and making any necessary assumptions): a) Calculate the probability that losses will be 160,000 or below. (6 marks) b) Calculate the S expected loss per year. (8 marks) c) Calculate, on the basis of expected value, how much would be saved if it was decided NOT to purchase the insurance cover. (6 marks) d) Now assume that an insurance with an aggregate deductible/excess of 160,000 can be purchased for an annual insurance premium of 50,000. Calculate the expected total cost of protection under the arrangement. (10 marks) With reference to your calculations so far for this question, offer your opinions on how the risk manager should choose between i) full retention, ii) the deductible/excess arrangement and iii) full insurance. (10 marks) e) f) Comment on factors, other than those mentioned in the question, that could influence the decision. (10 marks)