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Math 502. 3rd Homework. Due Friday, March 7, 2008. Name: .......................................................................................................................................................................
 

Summary: Math 502. 3­rd Homework. Due Friday, March 7, 2008.
Name: .......................................................................................................................................................................
1. Given a random sample of size n from the density
f(x|) =
3x2
3 if 0 < x < ,
0 else.
where > 0 is unknown parameter.
(a) Find the mle of .
(b) Find the method of moments estimator of .
(c) Which of the two estimators above has smallest mean square error?
2. Let X1, . . . , Xn denote a random sample from the density
f(x|) =
x-1
if 0 < x < 1,
0 else.
where > 0.
(a) Find the mle ^n of .
(b) Prove that this estimator is a consistent estimator of .
(c) Show that

  

Source: Arcones, Miguel A. - Department of Mathematical Sciences, State University of New York at Binghamton

 

Collections: Mathematics