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Math Help - Joint Distribution, expected value correlation of a graphed triangle

  1. #1
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    Joint Distribution, expected value correlation of a graphed triangle

    Let X and Y be the coordinates of a point chosen uniformly at random from the triangle that joins the points (0,1), (0,0), and (1,0).
    1) Find the joint distribution of X and Y.
    2) Determine the expected value of X and the expected value of Y (these are the expected coordinates of a point chosen at random).
    3) Find the correlation between X and Y.
    4) If the original units were measured in inches, would there be a different correlation if the units were changed to centimeters? Justify your answer mathematically?
    For 1, I got fX,Y(x,y)=2 and 2 I got fX(x)=22y and fY(y)=22x. Then for correlation in 3 I got 112(44x4y+4xy). I feel like I am forgetting something however and this should be different. For 4, I know this is unchanged but I am not sure how to show this. Any help is appreciated.
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  2. #2
    MHF Contributor
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    Re: Joint Distribution, expected value correlation of a graphed triangle

    Hey WUrunner.

    For the first one this will be a conditional distribution.

    You will have probabilities in the form of P(Y|X) or P(X|Y) and then you will have to use the relationship between conditional and joint distributions to get the actual distribution.

    Getting this will help you with the rest of the problems.
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