Answered step by step
Verified Expert Solution
Question
...
1 Approved Answer
2. Two independent measurements, X and Y , are taken of a quantity . Assume that E(X) = E(Y ) = , but X =
2. Two independent measurements, X and Y , are taken of a quantity . Assume that E(X) = E(Y ) = , but X = sd(X) and Y = sd(Y ) are unequal. The two measurements are combined by means of a weighted average to give Z = X + (1 )Y where is a scalar weight and [0, 1]. (a) Show that E(Z) = for any [0, 1]. (b) Show that V ar(Z) = 2 2 X + (1 w) 2 2 Y (c) Find in terms of X and Y that minimizes V ar(Z). (d) Under what circumstances is it better to use the average (X +Y )/2 than either X or Y alone?
Step by Step Solution
There are 3 Steps involved in it
Step: 1
![blur-text-image](https://dsd5zvtm8ll6.cloudfront.net/includes/images/document_product_info/blur-text-image.webp)
Get Instant Access with AI-Powered Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
![blur-text-image](https://dsd5zvtm8ll6.cloudfront.net/includes/images/document_product_info/blur-subtext-image.webp)
Step: 3
![blur-text-image](https://dsd5zvtm8ll6.cloudfront.net/includes/images/document_product_info/blur-subtext-image.webp)
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started