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

[asept]

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

 

[Defennder]

Just apply the definition of covariance and correlation. What are the formulae for both?

 

[asept]

Cov(X,Y) = E(XY) - E(X)E(Y)

 

[Defennder]

Yes correct, and now just apply the formulae for E(X), E(Y) and E(XY). What formulae should you use to evaluate each?