Let X1, X2,..., X, be a set of independent random variables each following the distribution with pdf 1 f(z]0) = ;z{2-0)/° on 0 < z < 1, with 0> 0. It can be shown that
Let X1, X2,..., X, be a set of independent random variables each following the distribution with pdf 1 f(z]0) = ;z{2-0)/° on 0 < z < 1, with 0> 0. It can be shown that
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Let X1, X2,..., Xn be a set of independent random variables each following
the distribution with pdf
f(피18) = z(1-0)/0 on 0<r<1,
with 0 > 0.
It can be shown that
E(X)
E(log X) = –0 and V(X)=
1+0'
(1+20)(1+0)²*
It can also be shown that the MLE of 0 is
- E, log X;
n
(a) According to the Central Limit Theorem, as given in Unit 1, what is the
asymptotic distribution of X, = (C1 X;)/n? State its parameter(s).
(b) Show that
d
1
dgz (0)
02
log r.
(c) Show that the Fisher information based on a single observation for 0 is
1
i(8)
02
(d) Use the result stated in part (c) to give the asymptotic distribution
of 6n-
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