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

Z = (X, Y) ∼ f_Z(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 f_x and f_y.

(b) Are X and Y independent?

(c) Find the conditional probability distributions f|_Y=y(x) and f|_X=x(y).