iid 1. Let Y1,..., Yn * Bernoulli(p). It can be shown using the properties of the MLE that when n is sufficiently large: yn(Ỹ – p) _d, N (0, 1) VÝ(1 – Ý) (a) Use this result to show that: - p) S Za/2 VÝ(1 P 21– a Y) (b) Use your answer in the previous part to derive an approximate 1 – a confidence interval for p.
iid 1. Let Y1,..., Yn * Bernoulli(p). It can be shown using the properties of the MLE that when n is sufficiently large: yn(Ỹ – p) _d, N (0, 1) VÝ(1 – Ý) (a) Use this result to show that: - p) S Za/2 VÝ(1 P 21– a Y) (b) Use your answer in the previous part to derive an approximate 1 – a confidence interval for p.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:iid
1. Let Y1,..., Yn * Bernoulli(p). It can be shown using the properties of the MLE that when n
is sufficiently large:
Vn(Y – P) d, N (0, 1)
VY(1 - Y)
(a) Use this result to show that:
Vn(Ÿ – p)
< Za/2
VÝ(1 – Y)
-Za/2 <
2 1– a
(b) Use your answer in the previous part to derive an approximate 1 – a confidence interval
for p.
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