Question: 7.2.14 An ecologist has to randomly select a point inside a circular region with radius R. She first samples the direction from the center of

7.2.14 An ecologist has to randomly select a point inside a circular region with radius R. She first samples the direction from the center of the region according to a uniform distribution on [ O", 360'1, and then samples the distance from the center according to U[O, R]. Find: (i) The density f(z, y) of the chosen points in ( 5 , y)

coordinates. (ii) The marginal distribution of X.

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