Find the variance, Consider a finite size population for N

Find the variance

Reference no: EM13245405

Consider a finite size population for N in which you want to study a variable y that takes a very small value for the first element of the sampling frame y1 and a very large value for the last element of the sampling frame yN. In order to estimate the average ? of this population μ, it is proposed, based on a Simple Random Sampling without replacement of size n, to have an estimator of the form:

?c is the estimator which has 3 parts:

?c = ? + c, if y1 belongs to the sample and yN does not belong to the sample

?c = ? - c, if y1 does not belong to the sample and yNbelongs to the sample

?c = ? ,And, in another case, where c is a positive constant.

a) Is ?c an unbiased estimator of μ?

b) Find the variance of ?c.

c) Are there values ??for c that make ?c to have less variance than ?? Does this contradict that Y is the best unbiased estimator of μ?

Reference no: EM13245405

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