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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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    Solution Summary

    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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