7. The following 4-state Markov model with constant intensities a, $ and y is used to model a pension scheme for male members aged 55. Age is defined as age last birthday on January 1". The states are w: Active, a: Preserved Benefit, b: Drawing pension and d: Dead. W B' b The following data were collected over an observation period covering a single calendar year on 1000 male members of the above pension scheme, all of whom are aged 55: Total waiting time in state w: 800 years Total number of transfers from state w to state a: 200 Total number of transfers from state w to state b: 200 Total number of transfers from state w to state c: 20 Find the likelihood function L(a, , y) for these data and hence find the maximum likelihood estimates of a, f and y