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In: Statistics and Probability

An arrow lands uniformly random on a circular target of radius r. Let y and z...

An arrow lands uniformly random on a circular target of radius r. Let y and z be the Cartesian coordinates. Thus, we can view y to be a realization of a random variable Y, and z a realization of another random variable Z.

(a) Are Y and Z independent?

(b) Are Y and Z uncorrelated?

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