# Joint Distribution, expected value correlation of a graphed triangle

• Dec 13th 2012, 02:56 AM
WUrunner
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.
• Dec 13th 2012, 08:57 PM
chiro
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.