Question: ) A point is chosen at random (according to a uniform PDF, i.e. sets with same areas are equally likely to include the chosen point)

) A point is chosen at random (according to a uniform PDF, i.e. sets with same areas are equally likely to include the chosen point) within a semicircle of the form {(x, y)|x2 + y2 r2, y 0} a. (10 pts) Find the joint PDF of the coordinates X and Y of the chosen point. b. (10 pts) Find the marginal PDF of Y and use it to find E[Y ]. Hint: For a given y [0, r], X can take values on the interval hpr2 y2, pr2 y2i

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