Random variables U and V are defined by
U = X + 2Y
V = X/Y
How do you find the inverse relationship?
Can anyone help?
Find the inverse relationship? Do you mean just solve for X and Y as functions of U and V? From U= X+ 2Y, X= U- 2Y. Putting that into V= X/Y, V= (U- 2Y)/Y= U/Y- 2 so that U/Y= V+ 2, Y/U= 1/(V+ 2) and, finally, Y= U/(V+ 2). Then X= U- 2Y= U- 2U/(V+ 2) which you could also write as X= (UV+ 2U- 2U)/(V+ 2)= UV/(V+ 2).