Question
Problem 4: Let X1, X2,..., Xn be a random sample of size n from the uniform
population given by
1
1 for 0
2
0 elsewhere.
1
f(x;0)
Show that if Y1 and Yn are the first and nth order statistic, any estimator
such that
1
1
n
2
2
can serve as a maximum likelihood estimator of 0. What does this say
the uniqueness of the maximum likelihood estimator
about
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Transcribed Image Text

Problem 4: Let X1, X2,..., Xn be a random sample of size n from the uniform population given by 1 1 for 0 2 0 elsewhere. 1 f(x;0) Show that if Y1 and Yn are the first and nth order statistic, any estimator such that 1 1 n 2 2 can serve as a maximum likelihood estimator of 0. What does this say the uniqueness of the maximum likelihood estimator about

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