Correlation with two independent variables

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Homework Help Overview

The discussion revolves around finding the correlation between the product of two independent variables, X and Y, and one of those variables, Y. The participants are exploring the implications of independence in the context of covariance and correlation.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to simplify the expression for covariance and questions whether the independence of X and Y implies the independence of X and Y squared. Other participants inquire about the proof of independence and seek clarification on the definition of "independent."

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of independence and its implications for covariance and correlation. There is no explicit consensus on the independence of X and Y squared, and further clarification is being sought.

Contextual Notes

Participants are working under the assumption that X and Y are independent, but there is uncertainty regarding the implications of this assumption on the relationship between X and Y squared.

rhuelu
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I would appreciate some help with this problem. Assuming X and Y are independent, I'm trying to find the correlation between XY and Y in terms of the means and standard deviations of X and Y. I'm not sure how to simplify cov(XY,Y)=E(XYY)-E(XY)E(Y)
=E(XY^2)-E(X)E(Y)^2.

If X and Y are independent, does it follow that X and Y^2 are independent. If this is the case, then covariance is zero --> correlation is zero. If this isn't the case I'm really not sure how to proceed. Any help is appreciated...
 
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rhuelu said:
I would appreciate some help with this problem. Assuming X and Y are independent, I'm trying to find the correlation between XY and Y in terms of the means and standard deviations of X and Y. I'm not sure how to simplify cov(XY,Y)=E(XYY)-E(XY)E(Y)
=E(XY^2)-E(X)E(Y)^2.

If X and Y are independent, does it follow that X and Y^2 are independent.
yes.
If this is the case, then covariance is zero --> correlation is zero. If this isn't the case I'm really not sure how to proceed. Any help is appreciated...
 


how would you prove this?
 


rhuelu said:
how would you prove this?

what do you mean by "independent"?
 

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