so in general, i am having difficulty in figuring out the range of a transformed variable. sometimes it's easy, i just plug in values and get the other values out, but sometimes i'm not seeing it. for example:
f(x)=4x3, for 0<x<1
and let U = (X-.5)2. Finding the pdf of U was not difficult, but finding the range is. the book says 0<u<.25.
The Attempt at a Solution
i can see that if i plug in 0 for x, i get .25, and if i plug in 1 for x, i get .25. i guess, in this range, i can see that the max is .25 and the min is 0. in general, is that how i find it? just take the min and max? that doesn't seem right to me.
another example would be with f(x) = 1, and let Y = X(1-X). finding the pdf wasn't too difficult, but again i'm having problem with the range. actually, the book gives the same answer, and the graph is pretty similar, just rotated. so, really, i don't know where to get the ranges.