Consider a log-linear regression model for the positive r.v. Y; whose value exceeds 50, satisfying log(Y; - 50) - BIti + Bar; + ci, i = 1, 2, - . ., n, where 1, . .., En are independent random errors with the same NV (0, o2) distribution, and x's are non-random design sample. Here B1, B2 and of > 0 are unknown parameters. (a) Find the maximum likelihood estimators of 31 and B2 in terms of Y1, Y2, . .., Yn and T1, X2, . . . , In; (b) Find the maximum likelihood estimator of o2; (c) Write down the maximum likelihood estimator of o; (d) Find the Fisher information matrix of 0 = (31, B2, 02)