Econ 506 Fall 2002 - Problem Set 1 solutions
1
Q .1
X x Y y
x
y
Define Z =
E[ X x ]
x
2
2
2
[
E[ X x ] Y y
x y
2
2
] + E[Y ]
y
y
2
2
0
1 2 XY + 1 0
xy 1
Now considering
Z=
X x Y y
+
x
y
We can show that
xy 1 Hence the result.
Q.5
U=X
Y
;V = Y X = UV ; Y
Econ 506 Fall 2002 - Problem Set 2 solutions Q.1 Consider Z i =
n 2
X i i , E[ Z i ] = 0,Var[ Z i ] = 1, i
2 Thus Z i is the sum of n squared standard normal variables and hence n i =1
Q.2 This question was discussed in great detail in the class, refer to
Econ 506 Fall 2012 - Sections 3 and 4 Selected solutions for problems assigned in
class
Q 4.40
Table at page 549 is used here, notice that the way the table is given it is giving
you the mass only one side and the question asks you a two tailed probabilit
Econ 506 Fall 2002 - Section 5 Selected solutions for problems assigned in class
Q 6.14
X = 81.2 , = 80 , n = 20 ,
Interval X C *
;
n
Where C = 1.96 (Value for 95 % confidence interval from Narmal Table)
The interval is (77.28,85.12)
Q 6.15
We have the In
Rutgers University
Practice Problems I Economics 506
Prof. Norman Swanson
1. Show that |XY | = 1.
2. Consider the regression model:
Yi = + Xi + i ,
where i is an error term.
Discuss conditional expection, variance, correlation, etc.
3. Write down and disc
Rutgers University
Practice Problems II Economics 506
Prof. Norman Swanson
2
1. Assume that Xi N (i , i ), i = 1, ., n, and that all Xi are independent, then prove that
n
[(Xi i )/i ] 2
n
Yi =
i=1
2. Assume that we are considering 2 models,
Yi = 1 + 1 Xi