This is a more general question about the transformation of a random variable. Say X is given as a certain distribution, and Y=g(X). If it asks to compute the pdf of Y, I am having trouble to determine the region of pdf of Y. (sorry I know this is confusing, let me have one example).
example: say Z is exponential (parameter 1/2), Y=exp(Z).
Then the cdf of Y=P(Z< lnz), pdf_Y =d/dz[ cdf_Y]=z^(-3/2). My question is what region does this answer defined?