Address the following questions clearly explaining your answers.

Three different drugs are being compared for their effectiveness in treating a certain illness. The mean number of days before the patient is discharged from hospital under each treatment is summarised below, together with the sample size and the sum of squares of the observations: Treatment Sample size Sample mean Sum of squares A 10 264 B 6 310 8 84 (i) For these three treatments, calculate estimates for the: (a) overall mean (b) common underlying variance. [4] (ii) Perform an analysis of variance to show that real differences exist among the three treatments at the 1% level. [3] (iii) Show that the mean number of days before discharge under treatment A is significantly better than under treatment B. [3] (iv) The cost per day for treatments A, B and C are $7.50, f5.85 and f14.95 respectively. Given that it can also be shown that there are significant differences between each pair of treatments, briefly advise the hospital on which treatment it should use. [2] [Total 12](i) Express in the form of symbols, and also explain in words, the expressions "death strain at risk", "expected death strain" and "actual death strain". [3] (ii) On 1 January 2001 an office issued a number of annual premium policies to a group of lives, each of whom was then aged exactly 45. All policies were for a term of 20 years and were of the following types: endowment assurances under which the sum assured was payable on survival to the end of the term or at the end of the year of earlier death temporary assurances under which the sum assured was payable only at the end of the year of death within the policy term pure endowments under which the only benefit payable is the sum assured on survival to the end of the policy term Assuming that there is no source of decrement other than death, calculate the profit or loss from mortality for the calendar year 2010 in respect of the policies issued to this group of lives, given the following information: Type of policy Sums assured in force Sums assured on I January 2010 by death during 2010 discontinued Endowment assurance E600,000 $4,000 Temporary assurance (200,000 $2,000 Pure endowment 180,000 $500 Reserving basis: AM92 Ultimate mortality, 4% pa interest. Ignore expenses. [12] [Total 15]