a) When is an estimator unbiased? Which assumptions do we need to establish unbiasedness of OLS estimates in a simple linear regression context? Explain. [10 Marks] b) What is a Type II error in statistical inference? [5 Marks] c) XYZ University graduate admission board requires graduate student candidates to take an English test and score at least 500. The test scores are normally distributed with a mean of 485 and standard deviation of 30. What percent of applicants pass? [10 Marks] d) Consider the savings function: sav = Bo + Binc + u u = inc e where e is a random variable with E(e)= 0 and Var(e) = 2. Also assume that e is independent of inc. i) Show that E(u|inc) = 0. [5 Marks] ii) Show that Var(u|inc) = inc. [5 Marks]