# Question

A pair of random variables is uniformly distributed over the ellipse defined by x2 + 4 y2 ≤ 1..

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

(b) Based on the results of part (a), find E [X], E [Y], Var (X), and Var (Y).

(c) Find the conditional PDFs,f X|Y (x | y) and f Y|X (y | x).

(d) Based on the results of part (c), find E [XY], Cov (X, Y), and pX, Y.

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

(b) Based on the results of part (a), find E [X], E [Y], Var (X), and Var (Y).

(c) Find the conditional PDFs,f X|Y (x | y) and f Y|X (y | x).

(d) Based on the results of part (c), find E [XY], Cov (X, Y), and pX, Y.

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