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1) Let X₁, X2, X3, ... Xn be a sequence of independent and identically distributed with the following probability density function f(x; 0) = {(0 + ¹ ((0+1)x-0-2 if 1 < x < 00 otherwise b) Use method of moments to find a statistic that we can use to estimate the parameter 8. c) Check if Y = is an unbiased estimator of 0 or not, where is the estimator obtained in b). d) Find the maximum likelihood estimator of the parameter 0. e) What is the fisher information in the sample of size n about the parameter 8.

1) Let X₁, X2, X3, ... Xn be a sequence of independent and identically distributed with the following probability density function f(x; 0) = {(0 + ¹ ((0+1)x-0-2 if 1 < x < 00 otherwise b) Use method of moments to find a statistic that we can use to estimate the parameter 8. c) Check if Y = is an unbiased estimator of 0 or not, where is the estimator obtained in b). d) Find the maximum likelihood estimator of the parameter 0. e) What is the fisher information in the sample of size n about the parameter 8.

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
Section13.3: Special Probability Density Functions
Problem 6E
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1) Let X₁, X2, X3, ... Xn be a sequence of independent and identically distributed with the following probability density function f(x; 0) = {(0 + ¹ S(0+1)x-0-2 if 1 < x < 00 otherwise b) Use method of moments to find a statistic that we can use to estimate the parameter 8. c) Check if Y = is an unbiased estimator of 0 or not, where ☎ is the estimator obtained in b). d) Find the maximum likelihood estimator of the parameter 0. e) What is the fisher information in the sample of size n about the parameter 0.
Transcribed Image Text:1) Let X₁, X2, X3, ... Xn be a sequence of independent and identically distributed with the following probability density function f(x; 0) = {(0 + ¹ S(0+1)x-0-2 if 1 < x < 00 otherwise b) Use method of moments to find a statistic that we can use to estimate the parameter 8. c) Check if Y = is an unbiased estimator of 0 or not, where ☎ is the estimator obtained in b). d) Find the maximum likelihood estimator of the parameter 0. e) What is the fisher information in the sample of size n about the parameter 0.
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