(b) Consider a sample of n iid observations that follow a Poisson distribution with unknown parameter A. For large n, what is the distribution of X, - A ? Use this result to construct an approximate two-sided 99%-confidence interval for A when n = 50 and 7 = 3. Two-sided means that your interval should not have -∞ or +∞ as an endpoint. You must include a detailed derivation of your confidence interval. Do not use the calculator (in particular, do not round any values) until the end of the calculation.
(b) Consider a sample of n iid observations that follow a Poisson distribution with unknown parameter A. For large n, what is the distribution of X, - A ? Use this result to construct an approximate two-sided 99%-confidence interval for A when n = 50 and 7 = 3. Two-sided means that your interval should not have -∞ or +∞ as an endpoint. You must include a detailed derivation of your confidence interval. Do not use the calculator (in particular, do not round any values) until the end of the calculation.
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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b) part only!
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![(a) For a sample of 15 iid normal observations with sample mean 7 = 10 and sample standard
deviation s = 3.2, construct a lower 99%-confidence bound for the population mean µ. You
must include a detailed derivation of your confidence bound.
(b) Consider a sample of n iid observations that follow a Poisson distribution with unknown
parameter A. For large n, what is the distribution of
X - A
?
VA/n
Use this result to construct an approximate two-sided 99%-confidence interval for A when
n = 50 and 7 = 3. Two-sided means that your interval should not have -o or +o as an
endpoint. You must include a detailed derivation of your confidence interval. Do not use the
calculator (in particular, do not round any values) until the end of the calculation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6ae73136-9df5-4db8-9008-250c2e6461dc%2F75849486-ad2f-42d7-bb29-2c97caddca85%2F2f9k41m_processed.png&w=3840&q=75)
Transcribed Image Text:(a) For a sample of 15 iid normal observations with sample mean 7 = 10 and sample standard
deviation s = 3.2, construct a lower 99%-confidence bound for the population mean µ. You
must include a detailed derivation of your confidence bound.
(b) Consider a sample of n iid observations that follow a Poisson distribution with unknown
parameter A. For large n, what is the distribution of
X - A
?
VA/n
Use this result to construct an approximate two-sided 99%-confidence interval for A when
n = 50 and 7 = 3. Two-sided means that your interval should not have -o or +o as an
endpoint. You must include a detailed derivation of your confidence interval. Do not use the
calculator (in particular, do not round any values) until the end of the calculation.
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