Question 1 (50%). To investigate the time required to do Assignment 2 of Simulation, one hundred observations X1, ..., X100 are recorded. On theoretical ground, it is postulated that the probability density function of the time required to do Assignment 2 is: 1 exp { - [In(x) - 8]~ } . I >0, f (x; B) = otherwise, where 8 is an unknown parameter. (a) Prove that the maximum-likelihood estimator of B is 8 = E In(X,). i=1 100 (a) Given that In(X;) = 100. Determine an approximate 95% confidence interval i=1 for B