How Do You Calculate Covariance and Correlation for X ~ U[0,1] and Y ~ U[0,X]?

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Homework Help Overview

The problem involves calculating the covariance and correlation between two random variables, X and Y, where X follows a uniform distribution on the interval [0,1] and Y follows a uniform distribution on the interval [0,X].

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the definitions and formulae for covariance and correlation, with an emphasis on the necessary expectations E(X), E(Y), and E(XY).

Discussion Status

Some participants have confirmed the formula for covariance and are exploring how to apply it to the specific distributions of X and Y. There is an ongoing examination of the appropriate formulae for calculating the expected values needed.

Contextual Notes

Participants are working within the constraints of the problem as posed, focusing on the definitions and calculations without providing complete solutions.

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I'm stuck on this problem:

Let X be uniform[0,1] and Y be uniform[0,X]. Calculate the covariance and correlation between X and Y.


thanks
 
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Just apply the definition of covariance and correlation. What are the formulae for both?
 
Cov(X,Y) = E(XY) - E(X)E(Y)
 
Yes correct, and now just apply the formulae for E(X), E(Y) and E(XY). What formulae should you use to evaluate each?
 

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