Estimation (ISS (Statistical Services) Statistics Paper II (Old Subjective Pattern)): Questions 1 - 8 of 14

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Question number: 1

» Estimation » Optimal Properties » Complete Statistics

Appeared in Year: 2014

Essay Question▾

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Define completeness. Verify whether Bin (1, p) is complete.

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Question number: 2

» Estimation » Estimation Methods » Methods of Moments

Appeared in Year: 2014

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For the Pareto distribution with pdf

Show that method of moments fails if 0 < λ < 1. State the method of moments estimator when λ > 1. Is it consistent? Justify your answer.

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Question number: 3

» Estimation » Estimation Methods » Methods of Moments

Appeared in Year: 2014

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X 1, X 2, …, X n be a random sample from U (0, θ). Obtain the moment estimator of θ. Also find its variance.

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Question number: 4

» Estimation » Estimation Methods » Maximum Likelihood

Appeared in Year: 2014

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X 1 , X 2 , …, X n are i. i. d. random variables from N (θ, 1) where θ is an integer. Obtain MLE of θ.

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Question number: 5

» Estimation » Optimal Properties » Sufficient Estimator

Appeared in Year: 2014

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Show that is not a sufficient estimator of the Bernoulli parameter θ.

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Question number: 6

» Estimation » Estimation Methods » Maximum Likelihood

Appeared in Year: 2014

Essay Question▾

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x1 , x 2 , …, x n be a random sample from the following distribution

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Question number: 7

» Estimation » Estimation Methods » Maximum Likelihood

Appeared in Year: 2014

Essay Question▾

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Let X be exponentially distributed with parameter θ. Obtain MLE of θ based on a sample of size n, from the above distribution.

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Question number: 8

» Estimation » Optimal Properties » Confidence Interval Estimation

Appeared in Year: 2015

Essay Question▾

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Let y 1, y 2, …, y n be a random sample from N (µ, σ 2) where µ and σ 2 are both unknown. Obtain a confidence interval of µ with confidence coefficient (1-α)

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