Let a r.vec. (X,Y) be uniformly distributed on the disk {(x,y) : x 2 + y 2

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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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