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Math Help - Random Variables

  1. #1
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    Random Variables

    A pair of random variables X and Y have continuous joint density function f(x,y) on (0,2)x(0,1) given by
    f(x,y) = K(x^3 + xy) 0<x<2 , 0<y<1.

    (a) Determine K
    (b) Determine E[X]
    (c) Determine V[X]
    (d) Determine E[XY]
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  2. #2
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    Quote Originally Posted by matty888 View Post
    A pair of random variables X and Y have continuous joint density function f(x,y) on (0,2)x(0,1) given by
    f(x,y) = K(x^3 + xy) 0<x<2 , 0<y<1.

    (a) Determine K
    (b) Determine E[X]
    (c) Determine V[X]
    (d) Determine E[XY]
    (a) Solve \int_{x=0}^{2} \int_{y = 0}^1 f(x, y) \, dy \, dx = 1 for K.


    (b) Calculate \int_{x=0}^{2} x \left( \int_{y = 0}^1 f(x, y) \, dy\right) \, dx.


    (c) Calculate E(X^2) = \int_{x=0}^{2} x^2 \left( \int_{y = 0}^1 f(x, y) \, dy\right) \, dx. Then Var(X) = E(X^2) - [E(X)]^2.


    (d) Calculate \int_{x=0}^{2} \int_{y = 0}^1 xy f(x, y) \, dy \, dx.
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    Thank you!!

    Thanks a million mr. fantastic you are very helpful.
    Could anyone confirm that my answers are right,not so sure myself
    (a) K = 1/5
    (b) 1.5466
    (c) 3.741155
    (d) 0.8177
    Thanks
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  4. #4
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    Quote Originally Posted by matty888 View Post
    Thanks a million mr. fantastic you are very helpful.
    Could anyone confirm that my answers are right,not so sure myself
    (a) K = 1/5
    (b) 1.5466
    (c) 3.741155
    (d) 0.8177
    Thanks
    (a) Correct.
    (b) Correct
    (c) I get different. What did you get for E(X^2)? I get 2.5333 (correct to 4 decimal places).
    (d) Correct.
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