Hey WUrunner (and thanks for fixing the latex up).
For V you can use the transformation theorem in probability and for U you can write things in terms of V.
Also is sin(2) meant to be sin(2*pi*Y)? If not then the tangent expression will be wrong.
Suppose X and Y are two independent random variables each distributed as $Uniform(0,1)$.
1) Find the joint distribution of X and Y.
2) Let and . Find the joint distribution
of U and V assuming that the transformation is one-to-one?
3) Find the marginal distributions of U and V?
For 1, I got that my distribution is 1 by multiplying the two distributions together. For 2, I have been getting stuck trying to get my equations in terms of X and Y to perform the transformation. I simplified and got but something seems wrong about this and am having trouble trying to get X. For 3, I am obviously stuck and even not totally sure on the support. Any help is appreciated.
Hey WUrunner (and thanks for fixing the latex up).
For V you can use the transformation theorem in probability and for U you can write things in terms of V.
Also is sin(2) meant to be sin(2*pi*Y)? If not then the tangent expression will be wrong.
Also you want to look at ratio distributions to get the distribution of a ratio of two independent variables:
Ratio distribution - Wikipedia, the free encyclopedia