Suppose X and Y are independent random variables with the same mean µ but possibly different variances σx2 and σy2.Imagine that X and Y are the averages of independent samples of size n1 and n2, respectively, taken from populations with the same mean µ and the same variance σ2. Apply below to identify the α that minimizes and the minimum value. Be sure to simplify both the new estimator and the minimum variance. Interpret the result.The variance of αX+(1-α)Y, which also has mean µ, is minimized with α=σy2/(σX2+σy2).

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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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Suppose X and Y are independent random variables with the same mean µ but possibly different variances σ_x² and σ_y².

Imagine that X and Y are the averages of independent samples of size n₁ and n₂, respectively, taken from populations with the same mean µ and the same variance σ².

Apply below to identify the α that minimizes and the minimum value. Be sure to simplify both the new estimator and the minimum variance. Interpret the result.

The variance of αX+(1-α)Y, which also has mean µ, is minimized with α=σ_y²/(σ_X²+σ_y²).

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