Question
Asked Oct 1, 2019
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Find fX(x) and fY (y) for each of the following joint pdfs.

(a) fX,Y (x, y) = xy, 0 ≤ x ≤ 2, 0 ≤ y ≤ 1.

(b) fX,Y (x, y) = 2/5 (2x + 3y), 0 ≤ x ≤ 1, 0 ≤ y ≤ 1.

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Expert Answer

Step 1

(a)

Provided joint pdf of (X, Y) is

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fxy (x,y) ,0x< 2,0 < y <1 The marginal pdf of X can be calculated as: fx(x)=fx(x.y)dy x = x 2 2

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Step 2

Similarly, marginal pdf of Y can be calculated as:

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f() (xy)d х 2 0 = y 2 0 =2y

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Step 3

(b)

Provided joint pdf of (X, ...

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2 (2.x+3y),0 sx1,0 y s1 .y)= fxy(x,y Marginal pdf of X for the provided function can be calculated as: (x) (xy)c (2x+3y)cy 3y2 2xy 2 4 3 5

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