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

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SUMMARY

The discussion focuses on calculating the covariance and correlation between two random variables, X and Y, where X follows a uniform distribution U[0,1] and Y follows a uniform distribution U[0,X]. The key formula for covariance is Cov(X,Y) = E(XY) - E(X)E(Y). Participants emphasize the need to apply the definitions of expected values E(X), E(Y), and E(XY) to derive the results accurately.

PREREQUISITES
  • Understanding of uniform distributions, specifically U[0,1] and U[0,X]
  • Knowledge of covariance and correlation definitions
  • Familiarity with expected value calculations
  • Basic probability theory concepts
NEXT STEPS
  • Learn how to calculate expected values for uniform distributions
  • Study the properties of covariance and correlation in probability theory
  • Explore examples of calculating Cov(X,Y) for different distributions
  • Review statistical software tools for performing covariance and correlation analysis
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Statisticians, data analysts, and students studying probability theory who need to understand the relationships between random variables and their statistical measures.

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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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