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Math Help - bivariate probability question

  1. #1
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    bivariate probability question

    two buses, A and B, operate on a route. A person arrives at a bus stop on this route at time 0. Let X and Y be the arrival times of bus A and bus B respectively, at this stop afterward. Suppose that X and Y are independent and have the density functions, respectively, by:

    f1(x) = 1/a, if 0<x<a
    0 otherwise

    f2(y) = 1/b, if 0<y<b
    0 otherwise

    where a,b>0 are constants. what is the probablity that bus B will arrive before bus A?


    THANKS
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  2. #2
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    Quote Originally Posted by lauren2988 View Post
    two buses, A and B, operate on a route. A person arrives at a bus stop on this route at time 0. Let X and Y be the arrival times of bus A and bus B respectively, at this stop afterward. Suppose that X and Y are independent and have the density functions, respectively, by:

    f1(x) = 1/a, if 0<x<a
    0 otherwise

    f2(y) = 1/b, if 0<y<b
    0 otherwise

    where a,b>0 are constants. what is the probablity that bus B will arrive before bus A?


    THANKS
    g(x, y) = f_1(x) \cdot f_2(y) = \frac{1}{ab} where 0 < x < a and 0 < y < b.

    The answer is therefore \frac{1}{ab} \cdot {R_{xy}} where R_{xy} is the area that lies above the line y = x that is enclosed by the axes and the lines x = a and y = b (this will depend on whether a > b or a < b and can be fuond using geometry - draw a diagram).
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