Show which of the estimators possess this property

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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IT HAS BEEN FOUND THAT A FLUCTUATING ELECTRIC CURRENT X AT ONE OF THE ESKOM SUBSTATIONS HAS A UNIFORM
PROBABILITY DISTRIBUTION,
f(x) =
a≤x≤b
otherwise
a+b
(b-a)²
WITH E(X) = AND Var (X) =
12
AS THE STATISTICIAN AT ESKOM AND HAVE BEEN GIVEN A RANDOM SAMPLE
OF 7 MEASUREMENTS X₁, X₂,,X, OF THE ELECTRIC CURRENT TO INFER ABOUT THE MEAN FLUCTUATION OVER A SPECIFIC
PERIOD. AFTER CAREFUL CONSIDERATION YOU HAVE IDENTIFIED THREE POSSIBLE ESTIMATORS
0₁ = X₁+X7, 0₂ = X₁ +2X₂+X AND 3 = X
3
Show which of the estimators possess this property
Transcribed Image Text:IT HAS BEEN FOUND THAT A FLUCTUATING ELECTRIC CURRENT X AT ONE OF THE ESKOM SUBSTATIONS HAS A UNIFORM PROBABILITY DISTRIBUTION, f(x) = a≤x≤b otherwise a+b (b-a)² WITH E(X) = AND Var (X) = 12 AS THE STATISTICIAN AT ESKOM AND HAVE BEEN GIVEN A RANDOM SAMPLE OF 7 MEASUREMENTS X₁, X₂,,X, OF THE ELECTRIC CURRENT TO INFER ABOUT THE MEAN FLUCTUATION OVER A SPECIFIC PERIOD. AFTER CAREFUL CONSIDERATION YOU HAVE IDENTIFIED THREE POSSIBLE ESTIMATORS 0₁ = X₁+X7, 0₂ = X₁ +2X₂+X AND 3 = X 3 Show which of the estimators possess this property
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