Problem 1. Suppose that we have a population model with a dependent variable y and the error term u (but no independent variable), as y Bo +u where Bo is a fixed parameter. Suppose that we have a random sample of size n, {: i =1, 2,…,n). following the population model. Suppose that the error u has an expected value of zero and variance of2. In other words,e(u)=0 and Var(u)=2 (a)Show that the sample mean of, i.e.= n Vi, is an unbiased estimator of po (b)What is the variance of y? What is the sampling variance of? (c)For all= 1, 2,…, n, define residuals as =i-y. Show that1n-1∑ is unbiased estimator of2.[hint: It is mathematical fact that(u-a)2]=(n-1)021(d)What is an appropriate estimator for the sampling variance of What is the standard error of?
