Question: Suppose a point in three- dimensional Cartesian space, (X, Y, Z) is equally likely to fall anywhere on the surface of the hemisphere defined by

Suppose a point in three- dimensional Cartesian space, (X, Y, Z) is equally likely to fall anywhere on the surface of the hemisphere defined by X2 + Y2 + Z2 = 1 and Z ≥ 0.
(a) Find the PDF of Z, fZ (z).
(b) Find the joint PDF of X and Y, f X, Y (x, y).

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