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Let f x y 3 2 x2 y 1

Let f(x, y) = 3/2, x2 ≤ y ≤ 1, 0 ≤ x ≤ 1, be the joint pdf of X and Y.

(a) Find P(0 ≤ X ≤ 1/2).

(b) Find P(1/2 ≤ Y ≤ 1).

(c) Find P(X ≥ 1/2, Y ≥ 1/2).

(d) Are X and Y independent? Why or why not?

(a) Find P(0 ≤ X ≤ 1/2).

(b) Find P(1/2 ≤ Y ≤ 1).

(c) Find P(X ≥ 1/2, Y ≥ 1/2).

(d) Are X and Y independent? Why or why not?

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