Question: Problem 5.65 Let (X, Y ) be uniformly distributed over the unit circle {(x, y) : x2 + y2 1}. Its joint distribution function

Problem 5.65 Let (X, Y ) be uniformly distributed over the unit circle {(x, y) : x2 + y2 ≤ 1}. Its joint distribution function is given in Problem 5.62. Find:

(a) the marginal distributions.

(b) Show that Cov(X, Y )=0, but that X and Y are not independent.

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