Answered: Consider a sample of n iid observations…

Consider a sample of n iid observations that follow a Poisson distribution with unknown parameter lambda. For large n, what is the distribution of (Xn − lamdba)/(lambda/n)^(1/2)?

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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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

b) Consider a sample of n iid observations that follow a Poisson distribution with unknown parameter lambda. For large n, what is the distribution of
(Xn − lamdba)/(lambda/n)^(1/2)?

Use this result to construct an approximate two-sided 99%-confidence interval for lamdba when n = 50 and x = 3. Two-sided means that your interval should not have −infinity or infinity as an endpoint. 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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