H Suppose that the number of property crimes committed by teenagers in the U.S. follows a distribution with mean and variance 02. (Note that uz0). You would like to learn about the average number of property crimes, but you find it too costly to study the entire population of teenagers, so you randomly select 10,000 people from the population, and record the number of property crimes every one of them committed. Comment on each of the proposed estimators of the population mean number of crimes, : (1) using the sample mean X as an estimator of the population mean 1a) Is X unbiased? Show formally and explain what this means intuitively. 1b) Is X efficient? Yes/no, and explain what efficiency means intuitively. (2) another estimator 1 using only the last two observations from your sample and calculated as: ^1 =1 2(XN-1 -2XN). 2a) Is ^1 unbiased? Show formally. 2b) Is 1consistent? Why or why not?