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1. Find the MLE of 0 based on a random sample X₁, X₂,..., Xn from each of the following p.d.f.'s. (a) where 0 < x < 1, 0 < 0, and 0 otherwise. (b) f(x|0) = 0x0-1 f(x0) = (0+1)x-0-2 where 1 < x, 0 < 0, and 0 otherwise. (c) where 0 < x, 0 <0, and 0 otherwise. f(z\0) = 0°xe-Đ

1. Find the MLE of 0 based on a random sample X₁, X₂,..., Xn from each of the following p.d.f.'s. (a) where 0 < x < 1, 0 < 0, and 0 otherwise. (b) f(x|0) = 0x0-1 f(x0) = (0+1)x-0-2 where 1 < x, 0 < 0, and 0 otherwise. (c) where 0 < x, 0 <0, and 0 otherwise. f(z\0) = 0°xe-Đ

Calculus For The Life Sciences
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.CR: Chapter 13 Review
Problem 3CR
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1. Find the MLE of based on a random sample X₁, X₂, ..., Xn from each of the following p.d.f.'s. (a) where 0 < x < 1, 0 < 0, and 0 otherwise. (b) f(x|0) = 0x0-1 f(x|0) = (0+1)x-0-2 where 1 < x, 0 < 0, and 0 otherwise. (c) where 0 < x, 0 <0, and 0 otherwise. (d) f(xz|0) = 02xe-0 f(x|0) = 0(10)x-1 for x = 1,2,..., 0 < 0 < 1, and 0 otherwise 2. Find the asymptotic variance of the MLE in each part of question 1.
Transcribed Image Text:1. Find the MLE of based on a random sample X₁, X₂, ..., Xn from each of the following p.d.f.'s. (a) where 0 < x < 1, 0 < 0, and 0 otherwise. (b) f(x|0) = 0x0-1 f(x|0) = (0+1)x-0-2 where 1 < x, 0 < 0, and 0 otherwise. (c) where 0 < x, 0 <0, and 0 otherwise. (d) f(xz|0) = 02xe-0 f(x|0) = 0(10)x-1 for x = 1,2,..., 0 < 0 < 1, and 0 otherwise 2. Find the asymptotic variance of the MLE in each part of question 1.
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