# m1_ak - Midterm Exam 1 Introduction to Econometrics - Fall...

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idtermExam1 Introduction to Econometrics - Fall 2006 You have one hour and 15 minutes to answer the questions below. You are not allowed to use any kind of notes or to consult formulas stored in your calculator; all the formulas you need are in the attached formulas sheet. The value of each question is given; manage your time remembering that the results of the exam will be curved. PLEASE SHOW YOUR WORK 1. (30 points) X and Y are two discrete random variables, with joint distribution given by: X Â Y 0 3 1 0 1 3 2 1 3 0 3 0 1 3 (a) (10 points) Calculate E [ Y | X = x ] for all possible values of X. E [ Y | X =1]=3 E [ Y | X =2]=0 E [ Y | X =3]=3 (b) (10 points) Show that cov ( X, Y )=0 . Note E [ X ]=2 and E [ Y ]=2 cov ( X, Y )= E [( X E [ X ]) ( Y E [ Y ])] = E [( X 2) ( Y 2)] =[ ( 1 2) (3 2)] 1 3 +[(2 2) (0 2)] 1 3 +[(3 2) (3 2)] 1 3 =[ ( 1) (1)] 1 3 +[(0)(0)] 1 3 +[(1)(1)] 1 3 = 1 3 + 1 3 Then: cov ( X, Y )=0 (c) (10 points) Given that cov ( X,Y )=0 , can we assert that E [ Y | X = x ]= E [ Y ] ? No, we can not assert that. In fact, we’ve shown that E [ Y | X =1] 6 = E ( Y ) , E [ Y | X =2 ] 6 = E ( Y ) and E [ Y | X =3] 6 = E ( Y ) . On the other hand, if it was true that E [ Y | X = x ]= E [ Y ] , we would know that cov ( X,Y )=0 . 2. (20 points) Manchester United is one of the most famous soccer teams in the World. Manchester’s stadium is called Old Tra f ord. For this exercise, assume that Old Tra f ord’s capacity is unlimited. In other words, there is no limit to the number of people that can f tinit . Some Econ 410 students are trying to estimate the e f ect of the price of tickets ( p i )onthenumbero f tickets sold ( q i ). Assume the following functional form represents the relationship between price and quantity: q i = β 0 + β 1 p i +

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## This note was uploaded on 07/28/2010 for the course ECON 410 taught by Professor Staff during the Fall '08 term at Wisconsin.

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m1_ak - Midterm Exam 1 Introduction to Econometrics - Fall...

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