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13 An insurer believes that the distribution of the number of claims on a particular type of policy is tyle binomial with parameters n=3 and p. A random sample of the number of claims on 153 policies revealed the following results: Number of claims 0 1 2 3 Number of policies 60 75 16 2 (i) Derive the maximum likelihood estimate of p. [4] (ii) Carry out a goodness of fit test for the binomial model specified in part (i) for the number of claims on each policy. [5] [Total 9] 14 In an investigation into a patient's red corpuscle count, the number of such corpuscles appearing in style each of 400 cells of a haemocytometer was counted. The results were as follows: No. of red blood 1 2 3 4 5 6 7 8 corpuscles No. of cells 40 66 93 94 62 25 14 5 1 It is thought that a Poisson distribution with mean / provides an appropriate model for this situation. (i) (a) Estimate / , the Poisson parameter. (b) Test the fit of the Poisson model. [8] (ii) For a healthy person, the mean count per cell is known to be equal to 3. For a patient with certain types of anaemia, the number of red blood corpuscles is known to be lower than this. Test whether this patient has one of these types of anaemia. (3] [Total 11] 15 In a recent study investigating a possible genetic link between individuals' susceptibility to tyle developing symptoms of AIDS, 549 men who had been diagnosed HIV positive were classified according to whether they carried two particular alleles (DRB1*0702 and DOA1*0201). The results were as follows: Free of Early Condition of individual Suffering Total symptoms symptoms from AIDS Alleles present 24 7 17 48 Alleles absent 98 93 310 501 Total 122 100 327 5491 A limited liability partnership differs from a limited company in that: A it is not a separate legal entity. B there must be one member with unlimited liability. it has no Memorandum or Articles of Association. O action cannot be taken against individual members for fraud and negligence. [2] .2 Which of the following is NOT true of a public company? A The company name must end in 'public limited company' or PLC or plc. B The ordinary shares must be quoted on the Stock Exchange. Ordinary shareholders have one vote per share held. The issued share capital must not be less than $50,000. [2] 3 Investors in the ordinary shares of a company have their liability limited to: the market price of the shares. the fully paid value of the shares. ona the nominal value of their holding. the capital value of their holding, less any dividends due. [2] 4 Explain the differences between a sole trader and a company. [5] Compare a partnership and a limited liability partnership. [5]