Maximum likelihood estimator, bias

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Let X1, X2, … be i.i.d. variables uniformily distributed on (0,20), and 0 > 0 is the unknown parameter. Define Gn and Hn as follows:

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Continuous Distributions
Mean
Variance
MomentGenerating
Function
1
; ? ? y ? ?2
?2 ? ?1 1
?1 + ?2
2
(?2 ? ?1 )2
12
et?2 ? et?1
t (?2 ? ?1 )

1
1
2
(y
?
J? exp ?
2? 2
? 2?
?? < y < +?
¿2
?
?2
(1 ? ?t)?1
??
?? 2
(1 ? ?t)??
v
2v
(1?2t)?v/2
?
?+?
(? + ?) (? + ? + 1)
Distribution
Uniform
Normal
Exponential
Probability Function
f (y) =
f (y) =
f (y) =

Gamma
Chi-square
f (y) =

1
??1 ?y/?
e
;
? y
(?)?
0
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