Test your understanding of sufficient statistics, complete statistics, and their applications in optimal estimation theory with 10 comprehensive questions
10
Total Questions
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Correct Answers
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Questions Attempted
Sufficient Statistics
2 questions
Question 1: Sample Mean Properties
For a population X ~ N(μ,σ²) with sample X₁, X₂, ..., Xₙ, which statement about the sample mean X̄ i...
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Question 4: Bernoulli Sufficient Statistic
For a population X ~ B(1,p) with sample X₁, X₂, ..., Xₙ, which statistic is sufficient for p?...
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Maximum Likelihood Estimation
1 questions
Question 2: Uniform Distribution MLE
For a population X ~ U(0,θ) with sample X₁, X₂, ..., Xₙ, the maximum likelihood estimator (MLE) is:...
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Mean Squared Error
1 questions
Question 3: MSE Decomposition
The mean squared error (MSE) formula is:...
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Cramér-Rao Bound
1 questions
Question 5: Poisson Fisher Information
For a population X ~ P(λ) with sample X₁, X₂, ..., Xₙ, the Cramér-Rao lower bound for unbiased estim...
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Least Squares Estimation
1 questions
Question 6: Linear Regression LSE
In the linear regression model Yᵢ = β₀ + β₁xᵢ + εᵢ, the least squares estimator for β₁ is:...
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Lehmann-Scheffé Theorem
1 questions
Question 7: UMVUE from Sufficient Complete Statistics
If T(X̃) is a sufficient complete statistic for θ and φ(X̃) is an unbiased estimator of g(θ), then E...
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Method of Moments
1 questions
Question 8: Exponential Distribution Moments
For a population X ~ E(λ) (exponential distribution) with sample X₁, X₂, ..., Xₙ, the method of mome...
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Efficiency
1 questions
Question 9: Efficient Estimator Properties
Which statement about efficient estimators is correct?...
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Unbiased Estimation
1 questions
Question 10: Normal Variance Estimation
For a population X ~ N(μ,σ²) with sample X₁, X₂, ..., Xₙ, which is an unbiased estimator of σ²?...
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