Question: The IRS is trying to estimate the average net worth of a large population of individuals. To do this the IRS takes a sample of size n from the population. Let \({{X}_{i}}\) and \({{Y}_{i}}\) denote respectively the 2003 taxable incoMeand the net worth of the ith individual in the sample. Let \({{\mu }_{x}}\) and \({{\mu }_{y}}\) be the population means

(a) How would you estimate \({{\mu }_{y}}\) from the sample \({{Y}_{1}},{{Y}_{2}},....,{{Y}_{n}}\) ?

(b) The IRS actually knows \({{\mu }_{x}}\). How would you use \({{\mu }_{x}}\) and the sample mean \(\bar{X}\) to refine the estimate obtained in part (a)?