Please help me to address the following economics questions. Thank you

The table below shows the cumulative claims incurred on a particular class of insurance policies, subdivided by accident year and development year. The total claims paid by the end of the Year 2007 is E2.4 million. Claims incurred Development year (f1000s) 0 2 3 2004 502 556 589 600 Accident 2005 487 565 593 year 2006 608 640 2007 551 (i) (a) State the assumptions underlying the basic chain ladder method. (b) Use the basic chain-ladder method to estimate the outstanding claims reserve as at 31 December 2007. 171 (1i) The earned premium in respect of each of the accident years 2004 - 2007 is shown in the following table. Accident year 2004 2005 2006 2007 Earned premium (f1000s) 750 770 905 865 Use the Bornhuetter-Ferguson method to estimate the outstanding claims reserve as at 31 December 2007. State any assumptions that you make. [7] [Total 14]An ARMA(2.1) process defined by: X, = --X,-2+Z, - -Z,-I where Z, ~ N (0.1) , has been running for a very long time. (i) Show that the process is weakly stationary. 121 (ii) (a) Find the autocorrelation function for lags 0, 1,2. (h) Show that the autocorrelation function at lag & (k =0,1,2....) can he expressed in the form: B where A and B are constants that you should specify. [12] (iii) Determine the probability distribution of X,. [3] [Total 17]