Suppose that E (0₂) = E(0₂) = = 0, var(0₂) = ₁, var(8₂) = ₂. Consider the following estimator ₂ = a₁ + (1 - a). Find all values of a such that the variance of estimator , is minimal, a. when estimators, and are independent. b. when cov(,,,) = c = 0.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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S 4
Suppose that E(8₂) = E() =
1 = 0, var(ô₂) = σ₂², var(§₂) = ₂². Consider the
following estimator = a₁ + (1 - a). Find all values of a such that the variance
of estimator 0, is minimal,
a. when estimators 0, and 0, are independent.
b. when cov(₁,₂)= = c = 0.
Transcribed Image Text:Suppose that E(8₂) = E() = 1 = 0, var(ô₂) = σ₂², var(§₂) = ₂². Consider the following estimator = a₁ + (1 - a). Find all values of a such that the variance of estimator 0, is minimal, a. when estimators 0, and 0, are independent. b. when cov(₁,₂)= = c = 0.
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