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.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.3: Special Probability Density Functions

Problem 26E

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