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Thread: CDF of distance between two points on a bounded line-segment.

  1. #1
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    CDF of distance between two points on a bounded line-segment.

    Hi all,

    I am trying to solve a paper, and I cannot understand (especially geometrically) how the limits
    are applied while finding CDF for the distance between two points (I understand how they are calculating CDF, but my point is
    how they have find the limits involved.). The question is attached as a figure.

    CDF of distance between two points on a bounded line-segment.-actual_prob.png
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  2. #2
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    Re: CDF of distance between two points on a bounded line-segment.

    see if this drawing helps

    CDF of distance between two points on a bounded line-segment.-clipboard.jpg
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  3. #3
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    Re: CDF of distance between two points on a bounded line-segment.

    Quote Originally Posted by romsek View Post
    see if this drawing helps

    Click image for larger version. 

Name:	clipboard.jpg 
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    Thanks for your message. However, some numerical help will be much appreciated. (note that my question is related to line segment only, not a rectangle!)
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  4. #4
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    Re: CDF of distance between two points on a bounded line-segment.

    Quote Originally Posted by sjaffry View Post
    Thanks for your message. However, some numerical help will be much appreciated. (note that my question is related to line segment only, not a rectangle!)
    you have a 2D joint distribution you are integrating over. The colored area is the total area of integration for $|x_1 - x_2|<\lambda$

    The three different colors represent the areas of integration corresponding to the three integrals in the highlighted area of the paper.

    Look a little harder, it's not that hard.
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