Z = (X, Y) f Z (x, y), which is 1/ inside the circle x 2

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Z = (X, Y) ∼ fZ(x, y), which is 1/π inside the circle x2 + y2 = 1, and 0 otherwise

(where π = 3.141 59…).

(a) Find the marginal probability distributions fx and fy.

(b) Are X and Y independent?

(c) Find the conditional probability distributions f|Y=y(x) and f|X=x(y).

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