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ECO 2400F1
Second Half of Fall 2010
Problem Set 1
Suggested Solutions
1.
(a) We observe X1 , . . . , Xn , where for each i cfw_1, . . . , n, Xi = + i . 1 , . . . , n are independent N (.1, 2 ) random
ECO 2400F1
Second Half of Fall 2010
Problem Set 4
Suggested Solutions
1.
(a)
n
i. Let T (x) x . If = 0, then T (X) N (0, 1). A level- test of H0 : 0
against H1 : > 0 would reject if T (x) z1 , where z
ECO 2400F1
Second Half of Fall 2010
Problem Set 3
Suggested Solutions
1.
(a)
i. Let h(Z) be an arbitrary function of Z. By iterated expectations,
E [h(Z)] = E [E [ h(Z)| Z]
= E [h(Z)E [ Y (Z)| Z]
= 0,
ECO 2400F1
Second Half of Fall 2010
Problem Set 2
Suggested Solutions
1.
(a)
i. When p = q = .1, we have the risk points given in Table 1 and plotted in Figure 1.
Table 1 and Figure 1 appear at the en
ECO 2400F1
Second Half of Fall 2010
Problem Set 6
Suggested Solutions
1.
(a)
i. The likelihood function is given by
cfw_
n
2
p (x, ) = (2)
n
1
2
(xi )
exp 2
2 i=1
,
cfw_(
)
which is maximized over
ECO 2400F1
Proposed Solutions to the Final Examination
17 December 2010
1. Suppose X1 , . . . , Xn are iid N (, 1). Consider the problem of estimating
the population mean , where the quality of the es
ECO 2400F1
Second Half of Fall 2010
Problem Set 5
Suggested Solutions
1.
(a) Let 1 , which allows the Weibull likelihood to be written as
( n )c1
(
)
n
n n
1
c
p(x, ) = c
xi
exp
xi .
i=1
i=1
For 1 <