Researchers propose a new treatment for a disease. Instead of recruitingpatients in the experiment to be a control group, researchers decide to use historical controls asbelow:

StudyID	#Patients	#Response
1	65	54
2	39	20
3	133	59
4	37	21
5	150	82

suppose there is no study-to-study variation, then the true response rates for studies should be equal, i.e.,1=2=...=5=. Please estimateand also calculate the standard error of the estimate. (b) [15 points] Suppose there is study-to-study variation, then the true response rates1, 2, ..., 5 for studies are iid with (, 2 ). An estimate ofis denoted by . Please calculate and its corresponding standard error. (c) [15 points] Suppose there is study-to-study variation, then the true response rates1, 2, ..., 5 for studies are iid with (, 2 ). Please estimate2