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Course: ECON 484, Spring 2012School: Rochester
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Math. Intro. Statistics & Econometrics 1-1 Problem Set 3 Due September 29 1. Solve Exercise 8 of Chapter 3 of Amemiya (1994). 2. Solve Exercise 4 Chapter of 4 of Amemiya (1994). 3. Solve Exercise 11 of Chapter 4 of Amemiya (1994). 4. Solve Exercise 19 of Chapter 4 of Amemiya (1994). Nee Yildiz s
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Math. Intro. Statistics & Econometrics
1-1
Problem Set 3
Due September 29
1. Solve Exercise 8 of Chapter 3 of Amemiya (1994).
2. Solve Exercise 4 Chapter of 4 of Amemiya (1994).
3. Solve Exercise 11 of Chapter 4 of Amemiya (1994).
4. Solve Exercise 19 of Chapter 4 of Amemiya (1994).
Nee Yildiz
s
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Rochester - ECON - 484
Intro. Math. Statistics & Econometrics1-1Nee YildizsProblem Set 3 - Solution1. (Ch3, Ex: 8) P (U + V < y ) =y0y v0ev eu dudv = 1 ey (1 + y ) = F (y )f (y ) = yeyuu+vTo get the joint density of X and Y , let (u, v ) =1 (x, y ) =D1 (x, y ) =
Rochester - ECON - 484
Intro. Math. Statistics & Econometrics1-1Problem Set 4Due October 61. Solve Exercise 1 of Chapter 5 of Amemiya (1994).2. Solve Exercise 2 of Chapter 5 of Amemiya (1994).3. Solve Exercise 5 of Chapter 5 of Amemiya (1994).4. Solve Exercise 6 of Chapt
Rochester - ECON - 484
Intro. Math. Statistics & Econometrics1-1Nee YildizsProblem Set 4 - Solution1. (Ch 5, Ex: 1) The probability that an ace will turn up is 1/6. So X is Binomial(5, 1/6).Then EX = 5/6 and V ar(X ) = 25/36. Moreover, P (X 4) = P (X = 4)+ P (X =5!5) =
Rochester - ECON - 484
Intro. Math. Statistics & Econometrics1-1Problem Set 5Due October 141. Solve Exercise 16 of Chapter 7 of Amemiya (1994).2. Solve Exercise 17 of Chapter 7 of Amemiya (1994).3. Solve Exercise 32 of Chapter 7 of Amemiya (1994).4. Solve Exercise 36 of
Rochester - ECON - 484
Intro. Math. Statistics & Econometrics1-1Nee YildizsProblem Set 5 - Solution1. (Ch 7, Ex: 16) The likelihood function is given by L = n=1 1 exp (|Xi |).i2(a) log L = n log 2 n=1 |Xi |. Thus, maximizer of the likelihood functioniis the same as th
Rochester - ECON - 484
Intro. Math. Statistics & Econometrics1-1Problem Set 6Due October 271. Solve Exercise 3 of Chapter 8 of Amemiya (1994).2. Solve Exercise 6 of Chapter 8 of Amemiya (1994).3. Solve Exercise 12 of Chapter 8 of Amemiya (1994).4. Solve Exercise 14 of Ch
Rochester - ECON - 484
Intro. Math. Statistics & Econometrics1-1Nee YildizsProblem Set 7Due November 141. (Amemiya, Ch. 9, Ex. 2) Suppose X has the following probability distribution:P (X = 1) = , P (X = 2) = 2, and P (X = 3) = 1 3, where [0, 1/3]. Weare to test H0 : =
Rochester - ECON - 484
Intro. Math. Statistics & Econometrics1-1Nee YildizsProblem Set 7 - Solution1. (a) There are eight possible tests: R1 = , R2 = cfw_1, R3 = cfw_2, R4 = cfw_3,R5 = cfw_1, 2, R6 = cfw_1, 3, R7 = cfw_2, 3, and R8 = cfw_1, 2, 3. For each of thesetests T
Rochester - ECON - 484
Intro. Math. Statistics & Econometrics1-1Nee YildizsProblem Set 8Due December 51. log wage = 0 + 1 married + 2 educ + z + u, E (u|married, educ, z ) = 0 wherez contains factors other than marital status and education that can aect wage.When 1 is s
Rochester - ECON - 484
Intro. Math. Statistics & Econometrics1Nee YildizsProblem Set 8 - Solution1. log (wage) = 0 + 1 married + 2 educ + z + u and E (u|married, educ, z ) = 0.(a) The above equation means that wage = eu e0 +1 married+2 educ+z . Since u isindependent of a
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Intro. Math. Statistics & Econometrics1-1Nee YildizsProblem Set 9Due December 121. Consider the systemyi1 = xi1 1 + ui1yi2 = xi2 2 + ui2 ,with the instrument matrixZi =ziT 010 ziT2,which is a 2 (L1 + L2 ) dimensional matrix, so that E [zi1
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