4. Suppose that estimators ₁ and ₂ are unbiased estimators of 0 and third estimator Ô3 = aê1 + (1 − a)ê₂; Var (ê¹) = 0² and Var (ô2₂) = 0₂; (a) Show that 3 is an unbiased estimator of (b) Find the Var (83) (c) Hence find the value of a that minimises the Var (03)

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 2EQ: 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed...
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4. Suppose that estimators ₁ and 2 are unbiased estimators of and third estimator
Ô3 = aÔ₁ + (1 − a)ô2; Var (ê¹) = 0² and Var (8₂) = 0;
(a) Show that 3 is an unbiased estimator of
(b) Find the Var (83)
(c) Hence find the value of a that minimises the Var (03)
- (03)
Transcribed Image Text:4. Suppose that estimators ₁ and 2 are unbiased estimators of and third estimator Ô3 = aÔ₁ + (1 − a)ô2; Var (ê¹) = 0² and Var (8₂) = 0; (a) Show that 3 is an unbiased estimator of (b) Find the Var (83) (c) Hence find the value of a that minimises the Var (03) - (03)
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