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es A1, A2,..., An have a common nonzero fr 2, and the correlation between any pair of r d hence prove that -1/(n-1) ≤p≤ 1. Q = o[X² + b (x₁) i=1 estimate of o2, find a and b. Hence show t Q n Σ i=1 2 (X₂ - X)² (1-p)(n-1)'

es A1, A2,..., An have a common nonzero fr 2, and the correlation between any pair of r d hence prove that -1/(n-1) ≤p≤ 1. Q = o[X² + b (x₁) i=1 estimate of o2, find a and b. Hence show t Q n Σ i=1 2 (X₂ - X)² (1-p)(n-1)'

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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4. The random variables X₁, X2, ..., Xn have a common nonzero mean µ, a common variance o², and the correlation between any pair of random variables is p. (a) Find var[X] and hence prove that −1/(n − 1) ≤p≤ 1. (b) If 2 n n Q = o £ x² + b (£x₁) ² Xi i=1 i=1 is an unbiased estimate of o2, find a and b. Hence show that, in this case, n (X¿ – X)² Q = Σ (1 − p) (n − 1) i=1
Transcribed Image Text:4. The random variables X₁, X2, ..., Xn have a common nonzero mean µ, a common variance o², and the correlation between any pair of random variables is p. (a) Find var[X] and hence prove that −1/(n − 1) ≤p≤ 1. (b) If 2 n n Q = o £ x² + b (£x₁) ² Xi i=1 i=1 is an unbiased estimate of o2, find a and b. Hence show that, in this case, n (X¿ – X)² Q = Σ (1 − p) (n − 1) i=1
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