These are cox model questions, the database is not needed. I just want to check my answer. Thank you!

Description: We consider the IMRAWIST dataset studied in Sloand et al., (Journal of Clinical Oncology, 2008, Vol. 26, No. 15, 25052511) and would like to model the hazard rate for time-todeath T based on the observed censored data {(Tg, 55) : i = 1, . . .,n} and the covariates {25 = (A,S,N,H,I)T : 2' = 1,...,n} using the Cox Proportional Hazard model Mt) = AoCt) exP{/3Tz,-}, (1) where, for the ith subject, A,- = age, 5,- = 0 or 1 if the subject is female or male, respectively, N, = Neutro (ANC), Pi = Platelets, and I, = 0 or 1 if the subject is from the IMRAW cohort or treated at NIH, respectively, Ao(t) is the continuous baseline hazard rate and )3 = (31,. .., 5)T is the vector of parameters. We assume that the uncensored time-to- death I? and the censoring time 0,; are independent, the subjects are independent and C, has density g(t) and cumulative distribution function G(t). Problems: (1) Suppose that the form of Ao(t) is unknown. (1.1) What is the expression of the conditional survival function Sg(t|Z5) = P(T,; > tIZi) in terms of Ao(t), Z; and )5\"? (1.2) What is the expression of the joint likelihood function of the observations {'1}, 6,, Z, : i: 1, . . .,n} as afunction of ADC), 13 and the {22,65,25 : i = 1, .. .,n}? (Note: The full joint likelihood may depend on g() and G(-) as well. You may write down the part of the joint likelihood that only involves the AD(-) and ,6 part) (2) Suppose that the baseline density fD(t), i.e., the corresponding density function for the baseline hazard rate Ag(t), has the expression f0(t) = obta'l exp(ibt\") for t 2 0 and some unknown parameters a > 0 and b > 0. (2.1) What is the expression of A5(t) in terms of a, I), Z, and ,3? (2.2) What is the expression of the conditional survival function S,(t|Z,v) = PCT; > t|Z,v) in terms of a, I), Z, and