Please help with attached question :

(HSD model). The health(H)-sickness(S)-death(D) model has 3 states {}, S, D) and tran- sition rates H P D The observations for a subject are . the times between successive transitions; . the numbers of transitions of each type. We define . V, = waiting time of the ith subject in the healthy state; . W, = waiting time of the ith subject in the sick state; . S; = number of transition H - S by the ith subject; . R; = number of transition S - H by the ith subject; . D; = number of transition H - D by the ith subject; . U; = number of transition S - D by the ith subject; . let V = EMI VA, W = EMI Wi, S = Em SAR = EM Ri, D = EM Di, U = EM . let v, w, s, r, d, u be observed values of V, W, S, R, D, U, respectively. (a) Write down the likelihood function. (b) Find the maximum likelihood estimators of the transition rates o, p, /, v. (c) State the large sample distribution of the estimators. (d) During a large study into rates of sickness: . 2, 710 healthy lives fell sick and 2, 490 sick lives recovered . 70 healthy lives and 120 sick lives died . For the whole group, the period of health and sickness totalled 41, 200 and 6, 700 years. Estimate the annual forces of transition between the states healthy, sick and dead. (e) Calculate, based on your estimates of the transition rates, the expected future life- times of healthy person and sick person