# Question

A pair of random variables has a joint PDF specified by

fX, Y( x, y) = d exp (–( ax2+ bxy+ cy2))

(a) Find the constant in terms of a, b, and c. Also, find any restrictions needed for a, b, and c themselves for this to be a valid PDF.

(b) Find the marginal PDFs, fX (x) and fY (y).

(c) Find Pr (X > Y).

fX, Y( x, y) = d exp (–( ax2+ bxy+ cy2))

(a) Find the constant in terms of a, b, and c. Also, find any restrictions needed for a, b, and c themselves for this to be a valid PDF.

(b) Find the marginal PDFs, fX (x) and fY (y).

(c) Find Pr (X > Y).

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