The attachments below contains three questions. Address them appropriately.

A set of crude forces of mortality (#, ) is to be graduated by reference to a standard table using the relationship /, = a/ +b. The parameters are to be determined using the method of weighted least squares. Assuming that all the crude rates are strictly positive, write down a formula for the expression to be minimised in this case and suggest an appropriate set of weights.A senior actuary wants to analyse the salaries of the 50 actuarial students employed by his company, using a linear model based on number of exam passes and years of experience. How would you express this model and the available data in terms of the notation given here?From first principles, derive expressions, which may involve an, i and P) (but no other compound interest functions), for each of the following functions: (i) a-P(assuming n is divisible by p ) [4] (ii) (la)= = AU - L'D [4] (iii) the present value of an annuity certain payable annually in arrears for a years, where the payment at the end of the year r is 72. [7] [Total 15]