(b) Consider an urn containing balls labelled 0, 1, 2, ..., n − 1 and the experiment - of drawing n of these balls uniformly and without replacement. Let X, denote the label of the ball drawn in the i-th step, 1 ≤ i ≤n. (i) For any 1 ≤ i ≤ n, what is E[X;] and V[X;]? Justify your answer. (ii) Compute Cov[X₁, X₂]. (iii) Suppose now that n is an unknown parameter and you observe the absolute difference between the labels of the first two balls, that is, Z := |X₁ – X₂|. Can you find an unbiased estimator of n based on Z? Justify your answer.
(b) Consider an urn containing balls labelled 0, 1, 2, ..., n − 1 and the experiment - of drawing n of these balls uniformly and without replacement. Let X, denote the label of the ball drawn in the i-th step, 1 ≤ i ≤n. (i) For any 1 ≤ i ≤ n, what is E[X;] and V[X;]? Justify your answer. (ii) Compute Cov[X₁, X₂]. (iii) Suppose now that n is an unknown parameter and you observe the absolute difference between the labels of the first two balls, that is, Z := |X₁ – X₂|. Can you find an unbiased estimator of n based on Z? Justify your answer.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![(b) Consider an urn containing balls labelled 0, 1, 2, n - 1 and the experiment
..9
of drawing n of these balls uniformly and without replacement. Let X, denote
the label of the ball drawn in the i-th step, 1 ≤ i ≤n.
(i) For any 1 ≤ i ≤ n, what is E[X;] and V[X;]? Justify your answer.
(ii) Compute Cov[X₁, X₂].
(iii) Suppose now that n is an unknown parameter and you observe the absolute
difference between the labels of the first two balls, that is, Z := |X₁ – X₂|.
Can you find an unbiased estimator of n based on Z? Justify your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe9cdea79-1c3e-46c9-9c06-26ef863fac64%2Fe5156a35-0e3d-4a10-ae34-fb41c5646393%2Fxun90e9_processed.png&w=3840&q=75)
Transcribed Image Text:(b) Consider an urn containing balls labelled 0, 1, 2, n - 1 and the experiment
..9
of drawing n of these balls uniformly and without replacement. Let X, denote
the label of the ball drawn in the i-th step, 1 ≤ i ≤n.
(i) For any 1 ≤ i ≤ n, what is E[X;] and V[X;]? Justify your answer.
(ii) Compute Cov[X₁, X₂].
(iii) Suppose now that n is an unknown parameter and you observe the absolute
difference between the labels of the first two balls, that is, Z := |X₁ – X₂|.
Can you find an unbiased estimator of n based on Z? Justify your answer.
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