Kindly help in answering the following questions. Please explain your answers step by step for full reward.

{ii {ii} {iii} {iv} a xed interest stock is redeemable at l'ld. in IS 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] Instead of purchasing the stock, the investor decides to agree a forward contract to buy the security in six yearsI time, immediately after the coupon payment then due. Calculate the forward price based on a risk-free rate of return of 6% pa e'ectiye and no arbitrage. The current price of the stock is that calculated in part {i}. [3] 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] Calculate the yield obtained if the investor sold the forward contract after three y-rs. [2] [Total 13] A discrete random variable has a probability function given by: X 2 4 5 P(X = x) 3-30 (i) Give the range of possible values for the unknown parameter o . [1] A random sample of 30 observations gave respective frequencies of 7, 6 and 17. (ii) Calculate the method of moments estimator of o . [3] (iii) Write down an expression for the likelihood of these data and hence show that the maximum likelihood estimate o satisfies the quadratic equation: 18062 + III a - 91 :0 [5] 8 32 (iv) Hence determine the maximum likelihood estimate and explain why the second root is rejected as a possible estimate of o. [3] [Total 12]