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Math Help - Joint Probability Function

  1. #1
    s7b
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    Joint Probability Function

    Hi, Can anyone help? I'm not even sure where to begin with this.

    The joint probability density function f(x,y) takes the value 1 inside the triangle T with the vertices (-1,0) (1,0) and (0,1) and f takes value 0 outside the triangle. Find the probability P(X greater or equal Y)


    I got as far as drawing a sketch of the triangle.
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  2. #2
    Flow Master
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    Quote Originally Posted by s7b View Post
    Hi, Can anyone help? I'm not even sure where to begin with this.

    The joint probability density function f(x,y) takes the value 1 inside the triangle T with the vertices (-1,0) (1,0) and (0,1) and f takes value 0 outside the triangle. Find the probability P(X greater or equal Y)


    I got as far as drawing a sketch of the triangle.
    The line passing through (-1, 0) and (0, 1) has equation y = x + 1.
    The line passing through (1, 0) and (0, 1) has equation y = -x + 1.

    \Pr(X \geq Y) = \int_{y = 0}^{y = 1/2} \int_{x = y}^{x = 1 - y} 1 \, dx \, dy.

    Note: The intersection point of y = x and y = -x + 1 is (1/2, 1/2).
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