Need an answer to the underneath asap

1. The lifetime of a type-A bulb is exponentially distributed with parameter A. The lifetime of a type-B bulb is exponentially distributed with parameter ,u, where a > A > 0. You have a box full of lightbulbs of the same type, and you would like to know whether they are of type A or B. Assume an a prion" probability of 1/3 that the box contains type-B lightbulbs. (a) You observe the value t1 of the lifetime, T1, of a lightbulb. A MAP decision rule implies that the lightbulb is of type A if and only if 151 Z a. Assuming that ,u, 2 2A, nd (1. Express your answer in terms of ,u, and A. (b) Assuming that ,u, 2 2A, What is the probability of error of the MAP estimator? (c) Assume that A = 2 and ,u = 3. Find the LMS estimate of T2, the lifetime of another lightbulb from the same box, based on observing T1 = 2. Assume that conditioned on the bulb type, bulb lifetimes are independent