2. Suppose that a physician can prescribe one of two drugs to patients newly diagnosed with lung cancer, druga or b. Suppose that the physician chooses drugs, denoted z, for 100 patients. He prescribes drug a to 25 patients (za) and drug b to the remaining 75 (z=b). You obtain data on these treatment decisions and observe the number of years, denoted y, that each patient lives after the treatment decision. Here are the data on the frequencies of different values of y: Treatment Years of Life after Treatment y=0 (z=a) 5 (z-b) 20 y=1 12 43 y = 2 or more 8 25 75 14455 25 55 20 100 When answering the questions below, consider the 100 patients to be the population of interest, not a sample drawn from a larger population. A. You are asked to predict y conditional on the event (za). Given the available data, what can you deduce about the best predictor of y conditional on (za), under absolute loss. B. Again you are asked to predict y conditional on the event (za). Given the available data, what can you deduce about the best predictor of y conditional on (za), under square loss? C. Let y(b) denote the numbers of years that a patient would live if he were prescribed drug b. Given the available data, what can you deduce about E[y(b)]? D. What can you deduce about M[y(b)]? E. Suppose that, at the time of treatment, the physician somehow knows each patient's values of [y(a), y(b)] and chooses treatments that maximize subsequent length of life. Thus the physician chooses z = a if y(a)>y(b) and z-bify(a)