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Joint Probability

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3. The joint probability density function of X and Y is given by
f(x, y) =6/7 (x2 + xy/2 ), 0 < x < 1, 0 < y < 2.

(a) Verify that this is indeed a joint density function.
(b) Compute the density function of X.
(c) Find P(X > Y ).
(d) Find P(Y > 1/2|X < 1/2).
(e) Find E(X).
(f) Find E(Y ).

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3. The joint probability density function of X and Y is given by
f(x, y) =6/7 (x2 + xy/2 ), 0 < x < 1, 0 < y < 2.

(a) Verify that this is indeed a joint density function.
(b) Compute the density function of X.
(c) Find P(X > Y ).
(d) Find P(Y > 1/2|X < 1/2).
(e) Find E(X).
(f) Find E(Y ).

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