Let X have the uniform distribution U(-1,3). How do you find the p.d.f. of ?
You need to be careful.
This one to one on 1<x<3 and two to one -1<x<1.
USE .
Now on -1<x<3.
Next notice that y's range is 0 to 9.
WHEN 0<y<1, we have a 2-1 mapping and both
.
So, for 0<y<1, we have
.
But when 1<y<9, we have a 1-1 mapping (with probability one)
So, while .
Thus for 1<y<9, we have
.
AND zero everwhere else.