2. (15%) In estimating the proportion p of the population (populations size N) with a spec ied characteristic, we got a simple random sample {311,312, - - ' ,yn} without replacement from the population and used 15 = 221:1 yi to estimate it, where if the ith element has the characteristic ,{1 y" 0 ifnot We know that E(yz) = E(y) = p, and 02 = VaT(y) = P P2- (1). Suppose that we use 62 = 13 152 as an estimator of 02. Is it an unbiased estimator of 02? If not, what is the bias? (2). Find an unbiased estimator of (72, based on your calculation in (1) Com- pare your constructed unbiased estimate with the one E531, where 5721 is the N sample variance