Question: A pair of random variables, (X, Y), is equally likely to fall anywhere within the region defined by |X| + |Y| 1. (a) Write

A pair of random variables, (X, Y), is equally likely to fall anywhere within the region defined by |X| + |Y| ≤ 1.
(a) Write the form of the joint PDF, fX,Y (x,y).
(b) Find the marginal PDFs, fX (x) and fY (y).
(c) Find and Pr (X > 1 / 2) and Pr (Y < 1 / 2)
(d) Find Pr (Y < 1 / 2|X > 1/ 2). Are the events {X > 1 / 2} and {Y < 1 / 2} independent?

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