6. Suppose the instructor wants to estimate the number of students cheating In 8 cless of size n. Each individual student i has a sensitive bit Xi0,1 (where 1 stands for cheating). Each student now sends the instructor A meserge Yi that depends on Xi and some random numbers which the individual can generate. Based on the Yi, the instructor wants to get an estimate of p=n1i=1nXi. One unified strategy is for each student to generate Yi such that: Yi={Xi1Xiwithprob.21+1withprob.211 where (0,21). (Notice when =0,Yi is Binomial (1/2) and reveals no information of p, and when =1/2, it protects no privacy of the student.) (a) (63) Show that A:=n1iYi is an unbiased estimator for p based on received message of Yi,i=1,n. (b) (6) What is the variance of A ? (c) (10) For a specific student i, the instructor is able to do hypothesis testing: Null: the student did not cheat, Alternative: the student cheated. Based on the rejection region Yi=1, what is the false positive rate ? In general, the higher is, the more private the procedure is. Show there is a trade-off between privacy and the variance of A