# Question: Let X and Y have the joint pdf f x y

Let X and Y have the joint pdf f(x, y) = x + y, 0 ≤ x ≤ 1, 0 ≤ y ≤ 1.

(a) Find the marginal pdfs fX(x) and fY(y) and show that f(x, y) ≠ fX(x)fY(y). Thus, X and Y are dependent.

(b) Compute

(i) μX,

(ii) μY,

(iii) σ2X, and

(iv) σ2Y.

(a) Find the marginal pdfs fX(x) and fY(y) and show that f(x, y) ≠ fX(x)fY(y). Thus, X and Y are dependent.

(b) Compute

(i) μX,

(ii) μY,

(iii) σ2X, and

(iv) σ2Y.

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