geometric probability: marginal densities

Find the density of the random variable \(X\) when the pair \( (X,Y) \) is chosen uniformly from the specified region in the plane in each case below.

  1. The diamond with vertices at \( (0,2), (-2,0), (0,-2), (2,0) \).
  2. The triangle with vertices \( (-2,0), (1,0), (0,2) \).

[Pitman p 277, #12]

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