For the following questions provide well explained answers.

An investigation took place into the mortality of pensioners. The investigation began on 1 January 2003 and ended on 1 January 2004. The table below gives the data collected in this investigation for & lives. Whether or not exit Date of birth Date of entry Date of exit was due to death (1) into observation from observation or other reason (0) 1 April 1932 1 January 2003 1 January 2004 0 1 October 1932 1 January 2003 1 January 2004 0 1 November 1932 1 March 2003 1 September 2003 1 January 1933 1 March 2003 1 June 2003 1 1 January 1933 1 June 2003 1 September 2003 0 1 March 1933 1 September 2003 1 January 2004 0 1 June 1933 1 January 2003 1 January 2004 0 1 October 1933 1 June 2003 1 January 2004 The force of mortality, /70, between exact ages 70 and 71 is assumed to be constant. (i) (a) Estimate the constant force of mortality, /70, using a two-state model and the data for the 8 lives in the table. (b) Hence or otherwise estimate 970 . [7] (ii) Show that the maximum likelihood estimate of the constant force, //70, using a Poisson model of mortality is the same as the estimate using the two-state model. [5] (iii) Outline the differences between the two-state model and the Poisson model when used to estimate transition rates. [3] [Total 15]