Consider thesimpleBernoullimodelwhereX1, ,Xn are independ ent andidenticallydistributedwith with (0, 1) being unknown a) ShowthattheMLEof is n Xn and thatthisisasymptoticallynormally distributedwith b) Considerthetransformation Yn sin1( pXn) Usethedeltamethodtofindthe asymptotic distributionof Yn P...

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Consider thesimpleBernoullimodelwhereX1, ...,Xn are independ- ent andidenticallydistributedwith with (0, 1) being unknown. a) ShowthattheMLEof

Question:

Consider thesimpleBernoullimodelwhereX1, ...,Xn are independ-

ent andidenticallydistributedwith

with μ ∈ (0, 1) being unknown.

a) ShowthattheMLEof μ is ˆμn = ¯Xn and thatthisisasymptoticallynormally distributedwith

image text in transcribed

b) Considerthetransformation Yn = sin−1(
p¯Xn). Usethedeltamethodtofindthe asymptotic distributionof Yn.

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Fundamentals Of Mathematical Statistics

ISBN: 9781032223827

1st Edition

Authors: Steffen Lauritzen

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Question Posted: Sep 19, 2024 08:01 PM

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Consider thesimpleBernoullimodelwhereX1, ...,Xn are independ- ent andidenticallydistributedwith with (0, 1) being unknown. a) ShowthattheMLEof

Question:

P(X = 1) 1-P(X = 0) =

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Fundamentals Of Mathematical Statistics

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