Estimating the bias of the population mean?

A simple random sample, y_1, y_2 ,..., y_n is selected without replacement from a population Y_1,Y_2, ...,Y_N where Y_1 is unusually small and Y_N is unusually large. We estimate the population mean, Y-bar, by the alternative estimator:





Estimate of (Y_a)-bar=


{y-bar +c ... if the sample contains population unit 1 but not N


{y-bar - c ... if the sample contains population unit N but not 1


{y-bar ... otherwise





where c is a fixed constant.





How do I show that the alternative estimator is unbiased?|||To estimate the bias of the population, you will need to use the appropriate sample/bias testing. Refer to links below:





http://en.wikipedia.org/wiki/Sampling_bi…


http://en.wikipedia.org/wiki/Selection_b…





Good luck!