SOLUTION MANUAL FOR END OF CHAPTER EXERCISES FOR: INTRODUCTION TO ECONOMETRICS, 3RD EDITION JAMES H. STOCK, AND MARK W. WATSON. CHAPTER 1-18 QUESTIONS AND ANSWERS 100% A+

SOLUTION MANUAL FOR END
OF CHAPTER EXERCISES FOR:
INTRODUCTION TO
ECONOMETRICS, 3RD EDITION
JAMES H. STOCK, AND MARK
W. WATSON. CHAPTER 1-18
QUESTIONS AND ANSWERS
100% A+

,Chapter 2
Review Of Probability

2.1. (A) Probability Distribution Function For Y

Outcome (Number Of Heads) Y 0 Y 1 Y 2
Probability 0.25 0.50 0.25

(B) Cumulative Probability Distribution Function For Y

Outcome (Number Of Heads) Y 0 0 Y 1 1 Y 2 Y 2
Probability 0 0.25 0.75 1.0

(C) = E(Y ) (0 0.25) 0.50) (2 0.25) 1.00 Fq,
D
. FY
Using Key Concept 2.3: Var(Y ) E(Y 2 ) E(Y )]2 ,
And
(Ui |Xi )
So That
Var(Y ) E(Y 2 ) E(Y )]2 1.50 (1.00)2 0.50.

2.2. We Know From Table 2.2 That Pr (Y 0) Pr (Y 1) Pr ( X 0)

Pr( X 1) So
(a) Y E(Y ) 0 Pr (Y 0) Pr (Y 1)
0
X E( X ) 0 Pr ( X 0) Pr ( X 1)
0 70
2
(b) E[( X )2 ]
X X

(0 0.70)2 Pr ( X 0) (1 0.70)2 Pr ( X 1)
2 2

2
E[(Y )2 ]
(0 0.78)2 Pr (Y 0) (1 0.78)2 Pr (Y 1)
2 2




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, Solutions to End-of-Chapter Exercises 3


(c) XY Cov (X , Y ) E[( X X )(Y Y )]
(0 0.70)(0 0.78) Pr( X 0, Y 0)
(0 Pr ( X Y 1)
(1 Pr ( X Y 0)
(1 Pr ( X Y 1)




Corr (X , Y ) XY
4

X Y
021 01716

2.3. For The Two New Random Variables W 3 6 X And V 20 7Y , We Have:
(a) E(V ) E(20 7Y ) 20 7E(Y ) 20 7
E(W ) E(3 6X ) 3 6E( X ) 3 6
2 2
(b) Var(3 6X ) 62 36
W X
2 2 2
V
Var(20 7Y ) Y
49
(c) WV Cov(3 6X , 20 7Y ) 6 Cov(X , Y )
WV
Corr (W , V ) 28

W V 756  84084
3 3
2.4. (A E( X ) 0 P) 3 P
)
P E( X K ) 0k P) k
(B P P
) 0.21 = 0.46.
E( X ) 0.3 , And Var(X) = E(X2 )−[E(X)]2 = 0.3 −0.09 = 0.21. Thus
(C =
)
Var( X E( X 2 E( X )]2 0.21 0.46. To Compute The
Skewness, Use The Formula From Exercise 2.21:
E( X )3 E( X 3 ) 3[E( X 2 )][E( X )] 2[E( X )]3
0.3 0.32 2 0.33 0.084
Alternatively, E( X )3 0.3)3 0.3] 0.3)3 0.7] 0.084
3 3 3
Thus, Skewness E( X )/ 0.084/0.46 0.87.
To Compute The Kurtosis, Use The Formula From Exercise 2.21:
E( X )4 E( X 4 ) 4[E( X )][E( X 3 )] 6[E( X )]2 [E( X 2 )] 3[E( X )]4
0.3 4 0.32 6 0.33 0.34 0.0777
Alternatively, E( X )4 0.3)4 0.3] 0.3)4 0.7] 0.0777
4 4 4
Thus, Kurtosis Is E( X )/ 0.0777/0.46
©2011 Pearson Education, Inc. Publishing as Addison Wesley

, 4 Stock/Watson • Introduction to Econometrics, Third Edition


2.5. Let X Denote Temperature In And Y Denote Temperature In Recall That Y 0 When X
32 And Y When X 212; This Implies Y (100/180) ( X 32) Or Y
o
(5/9) X. Using Key Concept 2.3, Y X f Implies That (5/9) 70
o
And X f Implies
Y (5/9) 7

2.6. The Table Shows That Pr ( X 0, Y 0) Pr ( X 0, Y 1)
Pr ( X 1, Y 0) Pr ( X 1, Y 1) Pr ( X 0) Pr ( X 1)

Pr(Y 0) Pr (Y 1)
(a) E(Y ) Y 0 Pr(Y 0) Pr (Y 1)
0
#(Unemployed)
(b) Unemployment Rate
#(Labor Force)
Pr (Y 0) 1 Pr(Y 1) 1 E(Y ) 1
(c) Calculate The Conditional Probabilities First:
Pr ( X 0, Y 0)
Pr (Y 0| X 0)
Pr ( X 0)
Pr ( X 0, Y 1)
Pr (Y 1| X 0)
Pr ( X 0)
Pr ( X 1, Y 0)
Pr (Y 0| X 1)
Pr ( X 1)
Pr ( X 1, Y 1)
Pr (Y 1| X 1)
Pr ( X 1)
The Conditional Expectations Are
E(Y|X 1) 0 Pr (Y 0| X 1) Pr (Y 1| X 1)
0
E(Y|X 0 Pr (Y 0| X Pr (Y 1|X 0)
0
(d) Use The Solution To Part (B),
E(Y|X
Unemployment Rate For Non-College Graduates 1 E(Y|X 0) 1 0.944 0.056
(e) The Probability That A Randomly Selected Worker Who Is Reported Being
Unemployed Is A College Graduate Is
Pr ( X 1, Y 0)
Pr ( X 1|Y 0)
Pr (Y 0)
The Probability That This Worker Is A Non-College Graduate Is
Pr ( X Y 1 Pr ( X 1|Y 1




©2011 Pearson Education, Inc. Publishing as Addison Wesley