3. Consider a population variable X, the average amount of money spent on entertainment by college students each week. This variable has mean and variance o. We observe an IID sample of size N, {X1,...,XN). We want to study the properties of the following class of estimators for the population mean: IM i=1 Xi, with c 1, a constant. (a) Is an unbiased estimators of the population mean ? [Prove it is, or prove it is not]. Does your answer depend on c? (b) What is the variance of ? How does this variance change with the value of the constant c?