Homework solutions
Math526
Spring 2004
Text book: Bickel-Doksum, 2nd edition
Assignment # 3
Section 4.5.
2. By assumption
What we need to prove is
P (X) 1
sup P (X) 0
0
This follows from the fact that for
P (X) 0 P (X)
Remark: In the case (X) is not co
Homework solutions
Math526
Spring 2004
Text book: Bickel-Doksum, 2nd edition
Assignment # 1
Section 4.3.
1. (a) The model is a exponential family satisfying condition in Example 4.3.3. So
the sample distribution
n
p(x, ) =
i=1
n
xi
e =
xi !
i=1
1
xi !
i
Homework solutions
Math526
Spring 2004
Text book: Bickel-Doksum, 2nd edition
Assignment # 4
Section 4.8.
1. (a). Note that
X Xn+1
N (0, 1)
n1 + 10
Solving
X Xn+1
z 1
1 + 1
2
n
for Xn+1 gives the (1 ) prediction interval for Xn+1 :
X
n1 + 10 z 1
, X+
2
n
Homework solutions
Math526
Spring 2004
Text book: Bickel-Doksum, 2nd edition
Assignment # 5
Section 5.1.
4. (a). The Chebyshev bound and Hoeding bounds are (Notice that 2 1 as
|X| 1) c( n ) and h( n ), respectively, where
1
and h(x) = 2 exp
x2
c(x) =
x2
2