Answer the following questions appropriately explaining every step of your working.

In an investigation into a patient's red corpuscle count, the number of such corpuscles appearing in each of 400 cells of a haemocytometer was counted. The results were as follows: No. of red blood 0 1 2 3 4 5 6 7 8 corpuscles No. of cells 40 66 93 94 62 25 14 5 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. [5] [Total 13](i) A fixed interest stock is redeemable at 106% in 15 years' time and pays interest at 9% pa payable half-yearly in arrears. Calculate the price an investor should pay to obtain a gross redemption yield of 9% pa. [2] (ii) Instead of purchasing the stock, the investor decides to agree a forward contract to buy the security in six years' time, immediately after the coupon payment then due. Calculate the forward price based on a risk-free rate of return of 6% pa effective and no arbitrage. The current price of the stock is that calculated in part (i). [3] (iii) Three years later, the price of the security is such that the gross redemption yield is still 9%. Calculate the value of the forward contract if the risk-free yield has not changed. [6] (iv) Calculate the yield obtained if the investor sold the forward contract after three years. [2] [Total 13]