Please can you help with the following question, it has been hard to get help for it :

Suppose that survival lifetime 7 has the Geometric distribution P(T = x) = (1 - 1)*-1, for x = 1,2, .... with 0 x) defines survival probability at time x, whereas d (x) denotes the mortality rate at time x, i.c., A(x) = P(T = x, 6 = 1 7 2x). Consider the likelihood function of n independent observations (7;, 6;), / = 1, ... .n L(D) = (1 -2)3-125. 1=1 (a) Show that under independent censoring', A (x) coincides with A(x) = P(T = xT 2 x) = 1. Hint: You may use the result of question 1(a) to establish the second equality. (b) Find the maximum likelihood estimation A. Show your working. Use the dataset in Table 1 to get the value of the estimator A. (c) Show that the observed Fisher information J(1) is given by J() = 1 1 - 1). [ (: -D). FI (d) Calculate an estimate Var(1) of the variance of A. Use the dataset. (e) Give the 95% confidence interval for 1