In a given population, n individuals are sampled randomly, with replacement, and each sampled individual is asked whether his/her salary is greater than some fixed threshold z. Assume that the salary of a randomly chosen individual has the exponential distribution with unknown parameter A . Asking whether the salary overcomes a given threshold rather than directly asking for the salary increases the number of people that are willing to answer and decreases the number of mistakes in the collected answers. Denote by X1, . .., An the binary responses of the n sampled individuals, so that X; E {0, 1} . We call the Xi censored data .(d) 1 point possible (graded) Convince yourself that f (in) is asymptotically normal and compute its asymptotic variance. V(f (1)) = You have used 0 of 4 attempts Save (6) 1 point possible (graded) What equation must 2 satisfy in order to minimize the asymptotic variance computed in part (d)? Write this equation in the form 9A (2) = z, where g)' is a function that depends on the unknown parameter A. 9A (Z) = (f) 1 point possible (graded) Let Y1, . . . ,Y be the salaries of the n sampled people. If one could actually observe Yl , . ..,Y;1 , what would be the Fisher information of Y, Iy (A), depending on A ? IY (A) = You have used 0 of 4 attempts Save (9) 1 point possible (graded) In the model where only the X1; '5 are observed (with fixed threshold 2: ), what is the Fisher information? Denote it by IX (A). IX 0') (h) 2 points possible (graded) Compare Iy (A) and I}; (A): O Iy (A) 2 IX (A) for all A O I}! (A) 5 IX (A) for all A O Iy (A) 2 IX (A) for some A, Iy (A)