If I were to define the coordinates $(X_{1},Y_{1})$ and $(X_{2},Y_{2})$ where
$$X_{1},X_{2} \sim \text{Unif}(0,30)\text{ and }Y_{1},Y_{2} \sim \text{Unif}(0,40).$$
How would I find the expected value of the distance between them?
I was thinking, since the distance is calculated by $\sqrt{(X_{1}-X_{2})^{2} + (Y_{1}-Y_{2})^{2}})$ would the expected value just be $(1/30 + 1/30)^2 + (1/40+1/40)^2$?
Best Answer
If I understand correctly what you're looking for, maybe this helps. You're trying to figure out the distance between to random points, who's X values are generated from unif(0,30) and Y values are generated from a unif (0,40). I just created a million RV's from each of those to distributions and then bound the x and the y to create a point for each of them. Then I calculated the distance between point 2 and 1 all the way to the distance between points 1,000,000 and 999,999. The average distance was 18.35855. Let me know if this isn't what you were looking for.