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b) Let X₁, X2, X3,...,Xn be a random sample of n from population X distributed with the f probability density function: 1 f(x; 0)=√√2π0 0, x² e 20, if -∞o < x < otherwise (i) Find the parameter space of 0. (ii) Find the maximum likelihood estimator of 0. (iii) Check whether or not the estimator obtained in (ii) is unbiased. (iv) Find the Fisher information in this sample of size n about the parameter 8.

b) Let X₁, X2, X3,...,Xn be a random sample of n from population X distributed with the f probability density function: 1 f(x; 0)=√√2π0 0, x² e 20, if -∞o < x < otherwise (i) Find the parameter space of 0. (ii) Find the maximum likelihood estimator of 0. (iii) Check whether or not the estimator obtained in (ii) is unbiased. (iv) Find the Fisher information in this sample of size n about the parameter 8.

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 39E: Assume that the probability that an airplane engine will fail during a torture test is 12and that...
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b) 2 / 3 100% + (ii) Use the Central Limit Theorem to compute P(0.5 < X < 1.5), for n = 30. (iii) Use the Chebychev inequality to find the value of k for P(0.5 < X < 1.5), if n = 30. Let X₁, X₂, X3,...,Xn be a random sample of n from population X distributed with the f probability density function: 1 f(x; 0)=√2π0 0, x² e 20 if -∞<x<∞ otherwise (i) Find the parameter space of 0. (ii) Find the maximum likelihood estimator of 0. (iii) Check whether or not the estimator obtained in (ii) is unbiased. (iv) Find the Fisher information in this sample of size n about the parameter 8.
Transcribed Image Text:b) 2 / 3 100% + (ii) Use the Central Limit Theorem to compute P(0.5 < X < 1.5), for n = 30. (iii) Use the Chebychev inequality to find the value of k for P(0.5 < X < 1.5), if n = 30. Let X₁, X₂, X3,...,Xn be a random sample of n from population X distributed with the f probability density function: 1 f(x; 0)=√2π0 0, x² e 20 if -∞<x<∞ otherwise (i) Find the parameter space of 0. (ii) Find the maximum likelihood estimator of 0. (iii) Check whether or not the estimator obtained in (ii) is unbiased. (iv) Find the Fisher information in this sample of size n about the parameter 8.
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