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Let X and Y be random variables with the joint pdf fX,Y(x,y) = 6x, 0 ≤...

Let X and Y be random variables with the joint pdf fX,Y(x,y) = 6x, 0 ≤ y ≤ 1−x, 0 ≤ x ≤1.

1. Are X and Y independent? Explain with a picture.

2. Find the marginal pdf fX(x).

3. Find P( Y < 1/8 | X = 1/2 )

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