Answer the questions in the attachments below clearly showing all the steps. Remember to include explanations.

The ordered remission times (in weeks) of 20 leukaemia patients are given in the table: VI N - VI N 8 8 11 12 12 15 17 22 23 Suppose the remission times can be regarded as a random sample from an exponential distribution with density: f(X; 1) = le-Ax (i) (a) Determine the maximum likelihood estimator 1 of A. (b) Obtain the large-sample approximate variance of 1. (c) Hence calculate an approximate 95% confidence interval for 1. (ii) Using the fact that 21aX has a 27, distribution, obtain an exact 95% confidence interval for 1, and comment briefly on how it compares with your interval in (1)(c).Butterflies of a certain species have short lives. After hatching, each butterfly experiences a lifetime defined by the following probability distribution: Lifetime (days) Probability 0.10 0.30 LAWN- 0.25 0.20 0.15 Calculate d; for / =1,2....,5 (to 3 decimal places) and sketch a graph of the discrete hazard function