8. Suppose that X₁, X₂, ..., X₂ is a random sample available from a population distributed as theBernoulli with parameter 0.(a) Find the Cramer-Rao lower bound variance for the estimator of 0.(b) Using the invariant property of maximum likelihood estimators,i. Find the estimator of 0² and show whether or not it is unbiased.ii. Find the Cramer-Rao lower bound variance for the estimator of 02 and its absoluteefficiency.

Given that X1, X2, . . ., Xn be a random sample from a population distributed as the Bernoulli with…

Answered: 8. Suppose that X₁, X2, ..., X₂ is a…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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Company A claims that the variance of the life of its appliances is less than the variance of the life of company B's appliances. A random sample of the lives of 27 of company A's appliances has a variance of 2.5 A random sample of the lives of 25 of company B's appliances has a variance of 2.8 At alphaαequals=0.10, can you support company A's claim? Complete parts (a) through (e). (a) Identify the claim and state Upper H 0H0 and Upper H Subscript aHa. Let sigma Subscript 1 Superscript 2σ21 represent the variance for company B's appliances and sigma Subscript 2 Superscript 2σ22 represent the variance for company A. A. Upper H 0H0: sigma Subscript 1 Superscript 2σ21less than<sigma Subscript 2 Superscript 2σ22, Upper H Subscript aHa: sigma Subscript 1 Superscript 2σ21greater than or equals≥sigma Subscript 2 Superscript 2σ22 B. Upper H 0H0: sigma Subscript 1 Superscript 2σ21less than or equals≤sigma Subscript 2 Superscript 2σ22, Upper H Subscript…
A manufacturer of sunflower oil uses machines to distribute liquid ingredients into bottles that move along a filling line. The machine that distributes is working properly when 8 ounces are distributed Suppose that the average amount distributed in a particular sample of 35 bottles is 7 91 0 ounces. Assume that the variance of the process is known to be 0.03 ounces squared. Is there evidence that the machine should be stopped (when not 8 ounces are distributed), and production wait for repairs? The lost production from a shutdown is potentially so great that management feels that the level of confidence in the analysis should be 99%
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The table below shows a sample of waiting times (in days) for a heart transplant for two age groups. At α=0.05, can you conclude that the variances of the waiting times differ between the two agegroups?
13
2b
From a sample of 25 observations, the estimate of the variance of the population was found to be 15.0 From another sample of 14 observations, the estimate variance was found to be 9.7 Can we accept the hypothesis that the two samples come from populations with equal variance, or must we conclude that the variance of the second population is smaller? Use the 0.01 level of significance.
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