Assume you are interested in the average income of aboriginals 18 years and up in Canada. Let income represent the wage of an aboriginal person 18 years and up living in Canada. For ease of presentation assume n, the sample size equals 5.Two possible estimator are proposed ̄ income =income1 + income2 + · · · + incomen n= income1 + income2 + income3 + income4 + income5 (1) 5income1 + incomen = income1 + income5 (2) 22 and Note: the second estimator only uses information from the first and last person drawn in the sample.a) Are both estimators random variables? Justify your answer.b) Calculate the mean of each estimator.c) Calculate the variance of each estimator. Note: since one is dealing with a random sample, there is no link between each draw. As such V ar(income1 + income2) = V ar(income1 + V ar(income2)d) which estimator is preferable? Justify your answer.e)Assumethefollowingsample,{incomei :i=1,…,n}={20000,100000,80000,60000,40000}. Calculate the estimate of each estimator.
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