Let X and Y be two jointly continuous random variables with joint probability distri- bution function (pdf) fxx (x, y) =CX 1≤ x + y ≤ 2, x ≥ 0, y ≥ 0. (a) Find the constant c. (b) Find the marginal pdfs of X and Y. (c) Obtain the exact value of P(X > Y). (d) Without actually performing the integration (just give the exact limits of the inte- gration), obtain the integral that expresses the P(Y> X2). Please provide a figure to show the region of interest.

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