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 *f**X*,*Y*(*x*,*y*)=2 and 2 I got *f**X*(*x*)=2−2*y* and *f**Y*(*y*)=2−2*x*. Then for correlation in 3 I got 112−(4−4*x*−4*y*+4*x**y*). 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.

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.