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

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To calculate the covariance and correlation between X ~ U[0,1] and Y ~ U[0,X], one must apply the definitions of covariance and correlation. The covariance is given by Cov(X,Y) = E(XY) - E(X)E(Y). The expected values E(X) and E(Y) can be derived from their uniform distributions, while E(XY) requires integration over the joint distribution of X and Y. The discussion emphasizes the need to correctly evaluate these expected values to find the desired covariance and correlation. Understanding these concepts is crucial for solving the problem effectively.
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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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