**Problem 6-66**Let \( x \) and \( y \) be independent random variables with variances \( \sigma_1^2 \) and \( \sigma_2^2 \), respectively. Consider the sum\[z = ax + (1-a)y \quad \text{where} \quad 0 \leq a \leq 1\]Find \( a \) that minimizes the variance of \( z \).

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Answered: 6-66 Let x and y be independent random…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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6-66 Let x and y be independent random variables with variances of and o2, respectively. Consider the sum z = ax + (1 − a)y Find a that minimizes the variance of z. Osasl