Statistics Graduate Level Quiz
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STATISTICAL INFERENCE
Question 1
of 10
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Let
X
1
,
…
,
X
n
X_1,\ldots,X_n
X
1
,
…
,
X
n
be independent with density
f
θ
(
x
)
=
1
/
θ
f_\theta(x)=1/\theta
f
θ
(
x
)
=
1/
θ
for
0
<
x
<
θ
0<x<\theta
0
<
x
<
θ
, where
θ
>
0
\theta>0
θ
>
0
. Write
M
=
max
i
X
i
M=\max_i X_i
M
=
max
i
X
i
. Which function of
M
M
M
is the UMVUE of
θ
2
\theta^2
θ
2
?
A
n
+
1
n
M
2
\frac{n+1}{n}M^2
n
n
+
1
M
2
B
n
+
2
n
M
2
\frac{n+2}{n}M^2
n
n
+
2
M
2
C
n
n
+
2
M
2
\frac{n}{n+2}M^2
n
+
2
n
M
2
D
(
n
+
1
n
M
)
2
\left(\frac{n+1}{n}M\right)^2
(
n
n
+
1
M
)
2
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