Let a r vec (X,Y) be uniformly distributed on the disk (x,y) x 2 y 2 4 Find the covariance Are X,Y independent Do the same for the uniform distribution on (x,y) x 2 x y 2 3y 20

Question: Let a r.vec. (X,Y) be uniformly distributed on the disk {(x,y) : x 2 + y 2 4}. Find the covariance. Are X,Y independent?

Let a r.vec. (X,Y) be uniformly distributed on the disk {(x,y) : x² + y² ≤ 4}. Find the covariance. Are X,Y independent? Do the same for the uniform distribution on {(x,y) :
x² +x+y²−3y≤ 20}.

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