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Question 7. 7(a). Let Xn be the sample mean of the random sample X₁, Xn from a Poisson distribution with mean 1. What is the limiting distribution of √(√√Xn - 1)? 7(b). Do question 7(a) for the case where X₁,, Xn are iid with the pdf f(x) = e-ª if x > 0 (otherwise f(x) = 0). Hint for 7(a) and 7(b): First use the CLT to find the limiting distribution of √n (Xn − 1), as nx, and then use the delta method.

Question 7. 7(a). Let Xn be the sample mean of the random sample X₁, Xn from a Poisson distribution with mean 1. What is the limiting distribution of √(√√Xn - 1)? 7(b). Do question 7(a) for the case where X₁,, Xn are iid with the pdf f(x) = e-ª if x > 0 (otherwise f(x) = 0). Hint for 7(a) and 7(b): First use the CLT to find the limiting distribution of √n (Xn − 1), as nx, and then use the delta method.

MATLAB: An Introduction with Applications
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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Question 7. 7(a). Let Xn be the sample mean of the random sample X₁,..., Xn from a Poisson distribution with mean 1. What is the limiting distribution of √n (√Xn - 1) ? 7(b). Do question 7(a) for the case where X₁,, Xn are iid with the pdf f(x) = e-ª if x > 0 (otherwise f(x) = 0). Hint for 7(a) and 7(b): First use the CLT to find the limiting distribution of √n (Xn − 1), a as n→ ∞, and then use the delta method.
Transcribed Image Text:Question 7. 7(a). Let Xn be the sample mean of the random sample X₁,..., Xn from a Poisson distribution with mean 1. What is the limiting distribution of √n (√Xn - 1) ? 7(b). Do question 7(a) for the case where X₁,, Xn are iid with the pdf f(x) = e-ª if x > 0 (otherwise f(x) = 0). Hint for 7(a) and 7(b): First use the CLT to find the limiting distribution of √n (Xn − 1), a as n→ ∞, and then use the delta method.
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