You start with the joint density of X1 and X2.
Then you solve for X1 and X2 in terms of the Y's.
You substitute into the first density and you multiply the absolute value of the jacobian.
This is just like the change to polar in calc3.
need help with this dont know were to start
question
suppose X1 and X2 are identically distributed independent standard normal random variables
write down the joint pdf of (X1, X2). determine the pdf of the linear transformation y1 =2x1-x2, y2=x1-2x2.
determine the correct range of this random variable.
any help appreciated
.... (1)
.... (2)
are a pair of linear simultaneous equations and at this level you are well and truly expected to know how to solve such a system. Perhaps use the elimination method ......? Start by multiplying equation (2) by -2 and then adding the two equations together .... ? etc.